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Bei uneigentlichen Integralen oder Integranden, die am Rand unstetig sind, braucht man stattdessen eine integrierbare Majorante ",[573,1235,1237,1258],{"className":1236},[576],[573,1238,1240],{"className":1239},[580],[582,1241,1242],{"xmlns":584},[586,1243,1244,1255],{},[589,1245,1246,1249,1251,1253],{},[592,1247,1248],{},"h",[669,1250,672],{"stretchy":671},[592,1252,700],{},[669,1254,677],{"stretchy":671},[596,1256,1257],{"encoding":598},"h(x)",[573,1259,1261],{"className":1260,"ariaHidden":603},[602],[573,1262,1264,1267,1270,1273,1276],{"className":1263},[607],[573,1265],{"className":1266,"style":729},[611],[573,1268,1248],{"className":1269},[616,617],[573,1271,672],{"className":1272},[737],[573,1274,700],{"className":1275},[616,617],[573,1277,677],{"className":1278},[744]," mit 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für alle ",[573,1560,1562,1575],{"className":1561},[576],[573,1563,1565],{"className":1564},[580],[582,1566,1567],{"xmlns":584},[586,1568,1569,1573],{},[589,1570,1571],{},[592,1572,594],{},[596,1574,594],{"encoding":598},[573,1576,1578],{"className":1577,"ariaHidden":603},[602],[573,1579,1581,1584],{"className":1580},[607],[573,1582],{"className":1583,"style":612},[611],[573,1585,594],{"className":1586},[616,617]," in einer Umgebung der betrachteten Stelle.",[564,1589,1590,1591,1619,1620,1648],{},"Hängen auch die Grenzen von ",[573,1592,1594,1607],{"className":1593},[576],[573,1595,1597],{"className":1596},[580],[582,1598,1599],{"xmlns":584},[586,1600,1601,1605],{},[589,1602,1603],{},[592,1604,594],{},[596,1606,594],{"encoding":598},[573,1608,1610],{"className":1609,"ariaHidden":603},[602],[573,1611,1613,1616],{"className":1612},[607],[573,1614],{"className":1615,"style":612},[611],[573,1617,594],{"className":1618},[616,617]," ab (differenzierbar in 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dazu:",[573,1650,1652],{"className":1651},[651],[573,1653,1655,1849],{"className":1654},[576],[573,1656,1658],{"className":1657},[580],[582,1659,1660],{"xmlns":584,"display":660},[586,1661,1662,1846],{},[589,1663,1664,1674,1698,1700,1702,1704,1706,1708,1710,1712,1714,1716,1718,1720,1723,1725,1727,1729,1731,1733,1735,1737,1739,1748,1750,1752,1754,1757,1759,1761,1763,1765,1767,1769,1771,1773,1775,1777,1783,1785,1787,1789,1792,1816,1830,1832,1834,1836,1838,1840,1842,1844],{},[950,1665,1666,1668],{},[592,1667,714],{},[589,1669,1670,1672],{},[592,1671,714],{},[592,1673,594],{},[682,1675,1676,1678,1688],{},[669,1677,686],{},[589,1679,1680,1682,1684,1686],{},[592,1681,689],{},[669,1683,672],{"stretchy":671},[592,1685,594],{},[669,1687,677],{"stretchy":671},[589,1689,1690,1692,1694,1696],{},[592,1691,692],{},[669,1693,672],{"stretchy":671},[592,1695,594],{},[669,1697,677],{"stretchy":671},[592,1699,695],{},[669,1701,672],{"stretchy":671},[592,1703,700],{},[669,1705,703],{"separator":603},[592,1707,594],{},[669,1709,677],{"stretchy":671},[709,1711,711],{},[592,1713,714],{},[592,1715,700],{},[669,1717,680],{},[592,1719,695],{},[669,1721,672],{"fence":603,"stretchy":603,"minsize":1722,"maxsize":1722},"1.2em",[592,1724,692],{},[669,1726,672],{"stretchy":671},[592,1728,594],{},[669,1730,677],{"stretchy":671},[669,1732,703],{"separator":603},[592,1734,594],{},[669,1736,677],{"fence":603,"stretchy":603,"minsize":1722,"maxsize":1722},[709,1738,711],{},[1740,1741,1742,1744],"msup",{},[592,1743,692],{},[669,1745,1747],{"mathvariant":956,"lspace":1746,"rspace":1746},"0em","′",[669,1749,672],{"stretchy":671},[592,1751,594],{},[669,1753,677],{"stretchy":671},[669,1755,1756],{},"−",[592,1758,695],{},[669,1760,672],{"fence":603,"stretchy":603,"minsize":1722,"maxsize":1722},[592,1762,689],{},[669,1764,672],{"stretchy":671},[592,1766,594],{},[669,1768,677],{"stretchy":671},[669,1770,703],{"separator":603},[592,1772,594],{},[669,1774,677],{"fence":603,"stretchy":603,"minsize":1722,"maxsize":1722},[709,1776,711],{},[1740,1778,1779,1781],{},[592,1780,689],{},[669,1782,1747],{"mathvariant":956,"lspace":1746,"rspace":1746},[669,1784,672],{"stretchy":671},[592,1786,594],{},[669,1788,677],{"stretchy":671},[669,1790,1791],{},"+",[682,1793,1794,1796,1806],{},[669,1795,686],{},[589,1797,1798,1800,1802,1804],{},[592,1799,689],{},[669,1801,672],{"stretchy":671},[592,1803,594],{},[669,1805,677],{"stretchy":671},[589,1807,1808,1810,1812,1814],{},[592,1809,692],{},[669,1811,672],{"stretchy":671},[592,1813,594],{},[669,1815,677],{"stretchy":671},[950,1817,1818,1824],{},[589,1819,1820,1822],{},[592,1821,957],{"mathvariant":956},[592,1823,695],{},[589,1825,1826,1828],{},[592,1827,957],{"mathvariant":956},[592,1829,594],{},[669,1831,672],{"stretchy":671},[592,1833,700],{},[669,1835,703],{"separator":603},[592,1837,594],{},[669,1839,677],{"stretchy":671},[709,1841,711],{},[592,1843,714],{},[592,1845,700],{},[596,1847,1848],{"encoding":598},"\\frac{d}{dt} 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6,2229,2232,2235,2238,2241],{"className":2151},[607],[573,2153],{"className":2154,"style":2056},[611],[573,2156,695],{"className":2157,"style":843},[616,617],[573,2159,2161],{"className":2160},[737],[573,2162,672],{"className":2163},[1357,2066],[573,2165,689],{"className":2166},[616,617],[573,2168,672],{"className":2169},[737],[573,2171,594],{"className":2172},[616,617],[573,2174,677],{"className":2175},[744],[573,2177,703],{"className":2178},[853],[573,2180],{"className":2181,"style":839},[748],[573,2183,594],{"className":2184},[616,617],[573,2186,2188],{"className":2187},[744],[573,2189,677],{"className":2190},[1357,2066],[573,2192],{"className":2193,"style":839},[748],[573,2195,2197,2200],{"className":2196},[616],[573,2198,689],{"className":2199},[616,617],[573,2201,2203],{"className":2202},[777],[573,2204,2206],{"className":2205},[781],[573,2207,2209],{"className":2208},[786],[573,2210,2212],{"className":2211,"style":2115},[790],[573,2213,2214,2217],{"style":2118},[573,2215],{"className":2216,"style":799},[798],[573,2218,2220],{"className":2219},[803,804,805,806],[573,2221,2223],{"className":2222},[616,806],[573,2224,1747],{"className":2225},[616,806],[573,2227,672],{"className":2228},[737],[573,2230,594],{"className":2231},[616,617],[573,2233,677],{"className":2234},[744],[573,2236],{"className":2237,"style":1127},[748],[573,2239,1791],{"className":2240},[1131],[573,2242],{"className":2243,"style":1127},[748],[573,2245,2247,2250,2325,2328,2396,2399,2402,2405,2408,2411,2414,2417,2420],{"className":2246},[607],[573,2248],{"className":2249,"style":1858},[611],[573,2251,2253,2256],{"className":2252},[767],[573,2254,686],{"className":2255,"style":773},[767,771,772],[573,2257,2259],{"className":2258},[777],[573,2260,2262,2317],{"className":2261},[781,782],[573,2263,2265,2314],{"className":2264},[786],[573,2266,2268,2291],{"className":2267,"style":1949},[790],[573,2269,2270,2273],{"style":794},[573,2271],{"className":2272,"style":799},[798],[573,2274,2276],{"className":2275},[803,804,805,806],[573,2277,2279,2282,2285,2288],{"className":2278},[616,806],[573,2280,689],{"className":2281},[616,617,806],[573,2283,672],{"className":2284},[737,806],[573,2286,594],{"className":2287},[616,617,806],[573,2289,677],{"className":2290},[744,806],[573,2292,2293,2296],{"style":812},[573,2294],{"className":2295,"style":799},[798],[573,2297,2299],{"className":2298},[803,804,805,806],[573,2300,2302,2305,2308,2311],{"className":2301},[616,806],[573,2303,692],{"className":2304},[616,617,806],[573,2306,672],{"className":2307},[737,806],[573,2309,594],{"className":2310},[616,617,806],[573,2312,677],{"className":2313},[744,806],[573,2315,826],{"className":2316},[825],[573,2318,2320],{"className":2319},[786],[573,2321,2323],{"className":2322,"style":2005},[790],[573,2324],{},[573,2326],{"className":2327,"style":839},[748],[573,2329,2331,2334,2393],{"className":2330},[616],[573,2332],{"className":2333},[737,985],[573,2335,2337],{"className":2336},[950],[573,2338,2340,2385],{"className":2339},[781,782],[573,2341,2343,2382],{"className":2342},[786],[573,2344,2346,2360,2368],{"className":2345,"style":1877},[790],[573,2347,2348,2351],{"style":1880},[573,2349],{"className":2350,"style":1005},[798],[573,2352,2354,2357],{"className":2353},[616],[573,2355,957],{"className":2356,"style":1015},[616],[573,2358,594],{"className":2359},[616,617],[573,2361,2362,2365],{"style":1021},[573,2363],{"className":2364,"style":1005},[798],[573,2366],{"className":2367,"style":1029},[1028],[573,2369,2370,2373],{"style":1903},[573,2371],{"className":2372,"style":1005},[798],[573,2374,2376,2379],{"className":2375},[616],[573,2377,957],{"className":2378,"style":1015},[616],[573,2380,695],{"className":2381,"style":843},[616,617],[573,2383,826],{"className":2384},[825],[573,2386,2388],{"className":2387},[786],[573,2389,2391],{"className":2390,"style":1922},[790],[573,2392],{},[573,2394],{"className":2395},[744,985],[573,2397,672],{"className":2398},[737],[573,2400,700],{"className":2401},[616,617],[573,2403,703],{"className":2404},[853],[573,2406],{"className":2407,"style":839},[748],[573,2409,594],{"className":2410},[616,617],[573,2412,677],{"className":2413},[744],[573,2415],{"className":2416,"style":839},[748],[573,2418,714],{"className":2419},[616,617],[573,2421,700],{"className":2422},[616,617],[564,2424,2425,2426,2454,2455,2483],{},"Ist ",[573,2427,2429,2442],{"className":2428},[576],[573,2430,2432],{"className":2431},[580],[582,2433,2434],{"xmlns":584},[586,2435,2436,2440],{},[589,2437,2438],{},[592,2439,695],{},[596,2441,695],{"encoding":598},[573,2443,2445],{"className":2444,"ariaHidden":603},[602],[573,2446,2448,2451],{"className":2447},[607],[573,2449],{"className":2450,"style":932},[611],[573,2452,695],{"className":2453,"style":843},[616,617]," unabhängig von ",[573,2456,2458,2471],{"className":2457},[576],[573,2459,2461],{"className":2460},[580],[582,2462,2463],{"xmlns":584},[586,2464,2465,2469],{},[589,2466,2467],{},[592,2468,594],{},[596,2470,594],{"encoding":598},[573,2472,2474],{"className":2473,"ariaHidden":603},[602],[573,2475,2477,2480],{"className":2476},[607],[573,2478],{"className":2479,"style":612},[611],[573,2481,594],{"className":2482},[616,617]," und nur die obere Grenze variabel, bleibt der Hauptsatz der Differential- und Integralrechnung übrig.",[564,2485,2486],{},"Als Rechentrick („Feynman-Trick“) führt man einen Parameter künstlich ein, leitet ab und erhält ein leichteres Integral.",[559,2488,2490],{"id":2489},"beispiele","Beispiele",[564,2492,2493,2785,2786,2844,2845,2897,2898,936,2957,3171,3172,3270,3271,3299,3300,3352,3353,3408,3409,2785,3552,3677,3678,647],{},[573,2494,2496,2555],{"className":2495},[576],[573,2497,2499],{"className":2498},[580],[582,2500,2501],{"xmlns":584},[586,2502,2503,2552],{},[589,2504,2505,2507,2509,2511,2513,2515,2526,2532,2534,2536,2538,2540],{},[592,2506,667],{},[669,2508,672],{"stretchy":671},[592,2510,594],{},[669,2512,677],{"stretchy":671},[669,2514,680],{},[682,2516,2517,2519,2523],{},[669,2518,686],{},[2520,2521,2522],"mn",{},"0",[2520,2524,2525],{},"1",[1740,2527,2528,2530],{},[592,2529,700],{},[592,2531,594],{},[709,2533,711],{},[592,2535,714],{},[592,2537,700],{},[669,2539,680],{},[950,2541,2542,2544],{},[2520,2543,2525],{},[589,2545,2546,2548,2550],{},[592,2547,594],{},[669,2549,1791],{},[2520,2551,2525],{},[596,2553,2554],{"encoding":598},"F(t) = \\int_0^1 x^t\\,dx = \\frac{1}{t + 1}",[573,2556,2558,2585,2701],{"className":2557,"ariaHidden":603},[602],[573,2559,2561,2564,2567,2570,2573,2576,2579,2582],{"className":2560},[607],[573,2562],{"className":2563,"style":729},[611],[573,2565,667],{"className":2566,"style":733},[616,617],[573,2568,672],{"className":2569},[737],[573,2571,594],{"className":2572},[616,617],[573,2574,677],{"className":2575},[744],[573,2577],{"className":2578,"style":749},[748],[573,2580,680],{"className":2581},[753],[573,2583],{"className":2584,"style":749},[748],[573,2586,2588,2592,2649,2652,2683,2686,2689,2692,2695,2698],{"className":2587},[607],[573,2589],{"className":2590,"style":2591},[611],"height:1.3648em;vertical-align:-0.3558em;",[573,2593,2595,2600],{"className":2594},[767],[573,2596,686],{"className":2597,"style":2599},[767,771,2598],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[573,2601,2603],{"className":2602},[777],[573,2604,2606,2640],{"className":2605},[781,782],[573,2607,2609,2637],{"className":2608},[786],[573,2610,2613,2625],{"className":2611,"style":2612},[790],"height:1.009em;",[573,2614,2616,2619],{"style":2615},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[573,2617],{"className":2618,"style":799},[798],[573,2620,2622],{"className":2621},[803,804,805,806],[573,2623,2522],{"className":2624},[616,806],[573,2626,2628,2631],{"style":2627},"top:-3.2579em;margin-right:0.05em;",[573,2629],{"className":2630,"style":799},[798],[573,2632,2634],{"className":2633},[803,804,805,806],[573,2635,2525],{"className":2636},[616,806],[573,2638,826],{"className":2639},[825],[573,2641,2643],{"className":2642},[786],[573,2644,2647],{"className":2645,"style":2646},[790],"height:0.3558em;",[573,2648],{},[573,2650],{"className":2651,"style":839},[748],[573,2653,2655,2658],{"className":2654},[616],[573,2656,700],{"className":2657},[616,617],[573,2659,2661],{"className":2660},[777],[573,2662,2664],{"className":2663},[781],[573,2665,2667],{"className":2666},[786],[573,2668,2671],{"className":2669,"style":2670},[790],"height:0.7936em;",[573,2672,2674,2677],{"style":2673},"top:-3.063em;margin-right:0.05em;",[573,2675],{"className":2676,"style":799},[798],[573,2678,2680],{"className":2679},[803,804,805,806],[573,2681,594],{"className":2682},[616,617,806],[573,2684],{"className":2685,"style":839},[748],[573,2687,714],{"className":2688},[616,617],[573,2690,700],{"className":2691},[616,617],[573,2693],{"className":2694,"style":749},[748],[573,2696,680],{"className":2697},[753],[573,2699],{"className":2700,"style":749},[748],[573,2702,2704,2708],{"className":2703},[607],[573,2705],{"className":2706,"style":2707},[611],"height:1.2484em;vertical-align:-0.4033em;",[573,2709,2711,2714,2782],{"className":2710},[616],[573,2712],{"className":2713},[737,985],[573,2715,2717],{"className":2716},[950],[573,2718,2720,2773],{"className":2719},[781,782],[573,2721,2723,2770],{"className":2722},[786],[573,2724,2727,2747,2755],{"className":2725,"style":2726},[790],"height:0.8451em;",[573,2728,2729,2732],{"style":1001},[573,2730],{"className":2731,"style":1005},[798],[573,2733,2735],{"className":2734},[803,804,805,806],[573,2736,2738,2741,2744],{"className":2737},[616,806],[573,2739,594],{"className":2740},[616,617,806],[573,2742,1791],{"className":2743},[1131,806],[573,2745,2525],{"className":2746},[616,806],[573,2748,2749,2752],{"style":1021},[573,2750],{"className":2751,"style":1005},[798],[573,2753],{"className":2754,"style":1029},[1028],[573,2756,2758,2761],{"style":2757},"top:-3.394em;",[573,2759],{"className":2760,"style":1005},[798],[573,2762,2764],{"className":2763},[803,804,805,806],[573,2765,2767],{"className":2766},[616,806],[573,2768,2525],{"className":2769},[616,806],[573,2771,826],{"className":2772},[825],[573,2774,2776],{"className":2775},[786],[573,2777,2780],{"className":2778,"style":2779},[790],"height:0.4033em;",[573,2781],{},[573,2783],{"className":2784},[744,985]," für ",[573,2787,2789,2810],{"className":2788},[576],[573,2790,2792],{"className":2791},[580],[582,2793,2794],{"xmlns":584},[586,2795,2796,2807],{},[589,2797,2798,2800,2803,2805],{},[592,2799,594],{},[669,2801,2802],{},">",[669,2804,1756],{},[2520,2806,2525],{},[596,2808,2809],{"encoding":598},"t > -1",[573,2811,2813,2831],{"className":2812,"ariaHidden":603},[602],[573,2814,2816,2819,2822,2825,2828],{"className":2815},[607],[573,2817],{"className":2818,"style":1211},[611],[573,2820,594],{"className":2821},[616,617],[573,2823],{"className":2824,"style":749},[748],[573,2826,2802],{"className":2827},[753],[573,2829],{"className":2830,"style":749},[748],[573,2832,2834,2838,2841],{"className":2833},[607],[573,2835],{"className":2836,"style":2837},[611],"height:0.7278em;vertical-align:-0.0833em;",[573,2839,1756],{"className":2840},[616],[573,2842,2525],{"className":2843},[616],". Für ",[573,2846,2848,2866],{"className":2847},[576],[573,2849,2851],{"className":2850},[580],[582,2852,2853],{"xmlns":584},[586,2854,2855,2863],{},[589,2856,2857,2859,2861],{},[592,2858,594],{},[669,2860,2802],{},[2520,2862,2522],{},[596,2864,2865],{"encoding":598},"t > 0",[573,2867,2869,2887],{"className":2868,"ariaHidden":603},[602],[573,2870,2872,2875,2878,2881,2884],{"className":2871},[607],[573,2873],{"className":2874,"style":1211},[611],[573,2876,594],{"className":2877},[616,617],[573,2879],{"className":2880,"style":749},[748],[573,2882,2802],{"className":2883},[753],[573,2885],{"className":2886,"style":749},[748],[573,2888,2890,2894],{"className":2889},[607],[573,2891],{"className":2892,"style":2893},[611],"height:0.6444em;",[573,2895,2522],{"className":2896},[616]," sind ",[573,2899,2901,2919],{"className":2900},[576],[573,2902,2904],{"className":2903},[580],[582,2905,2906],{"xmlns":584},[586,2907,2908,2916],{},[589,2909,2910],{},[1740,2911,2912,2914],{},[592,2913,700],{},[592,2915,594],{},[596,2917,2918],{"encoding":598},"x^t",[573,2920,2922],{"className":2921,"ariaHidden":603},[602],[573,2923,2925,2928],{"className":2924},[607],[573,2926],{"className":2927,"style":2670},[611],[573,2929,2931,2934],{"className":2930},[616],[573,2932,700],{"className":2933},[616,617],[573,2935,2937],{"className":2936},[777],[573,2938,2940],{"className":2939},[781],[573,2941,2943],{"className":2942},[786],[573,2944,2946],{"className":2945,"style":2670},[790],[573,2947,2948,2951],{"style":2673},[573,2949],{"className":2950,"style":799},[798],[573,2952,2954],{"className":2953},[803,804,805,806],[573,2955,594],{"className":2956},[616,617,806],[573,2958,2960,3004],{"className":2959},[576],[573,2961,2963],{"className":2962},[580],[582,2964,2965],{"xmlns":584},[586,2966,2967,3001],{},[589,2968,2969,2979,2985,2987,2993,2996,2999],{},[950,2970,2971,2973],{},[592,2972,957],{"mathvariant":956},[589,2974,2975,2977],{},[592,2976,957],{"mathvariant":956},[592,2978,594],{},[1740,2980,2981,2983],{},[592,2982,700],{},[592,2984,594],{},[669,2986,680],{},[1740,2988,2989,2991],{},[592,2990,700],{},[592,2992,594],{},[592,2994,2995],{},"ln",[669,2997,2998],{},"⁡",[592,3000,700],{},[596,3002,3003],{"encoding":598},"\\frac{\\partial}{\\partial t} x^t = x^t \\ln x",[573,3005,3007,3124],{"className":3006,"ariaHidden":603},[602],[573,3008,3010,3014,3086,3115,3118,3121],{"className":3009},[607],[573,3011],{"className":3012,"style":3013},[611],"height:1.2251em;vertical-align:-0.345em;",[573,3015,3017,3020,3083],{"className":3016},[616],[573,3018],{"className":3019},[737,985],[573,3021,3023],{"className":3022},[950],[573,3024,3026,3075],{"className":3025},[781,782],[573,3027,3029,3072],{"className":3028},[786],[573,3030,3033,3050,3058],{"className":3031,"style":3032},[790],"height:0.8801em;",[573,3034,3035,3038],{"style":1001},[573,3036],{"className":3037,"style":1005},[798],[573,3039,3041],{"className":3040},[803,804,805,806],[573,3042,3044,3047],{"className":3043},[616,806],[573,3045,957],{"className":3046,"style":1015},[616,806],[573,3048,594],{"className":3049},[616,617,806],[573,3051,3052,3055],{"style":1021},[573,3053],{"className":3054,"style":1005},[798],[573,3056],{"className":3057,"style":1029},[1028],[573,3059,3060,3063],{"style":2757},[573,3061],{"className":3062,"style":1005},[798],[573,3064,3066],{"className":3065},[803,804,805,806],[573,3067,3069],{"className":3068},[616,806],[573,3070,957],{"className":3071,"style":1015},[616,806],[573,3073,826],{"className":3074},[825],[573,3076,3078],{"className":3077},[786],[573,3079,3081],{"className":3080,"style":1057},[790],[573,3082],{},[573,3084],{"className":3085},[744,985],[573,3087,3089,3092],{"className":3088},[616],[573,3090,700],{"className":3091},[616,617],[573,3093,3095],{"className":3094},[777],[573,3096,3098],{"className":3097},[781],[573,3099,3101],{"className":3100},[786],[573,3102,3104],{"className":3103,"style":2670},[790],[573,3105,3106,3109],{"style":2673},[573,3107],{"className":3108,"style":799},[798],[573,3110,3112],{"className":3111},[803,804,805,806],[573,3113,594],{"className":3114},[616,617,806],[573,3116],{"className":3117,"style":749},[748],[573,3119,680],{"className":3120},[753],[573,3122],{"className":3123,"style":749},[748],[573,3125,3127,3130,3159,3162,3165,3168],{"className":3126},[607],[573,3128],{"className":3129,"style":2670},[611],[573,3131,3133,3136],{"className":3132},[616],[573,3134,700],{"className":3135},[616,617],[573,3137,3139],{"className":3138},[777],[573,3140,3142],{"className":3141},[781],[573,3143,3145],{"className":3144},[786],[573,3146,3148],{"className":3147,"style":2670},[790],[573,3149,3150,3153],{"style":2673},[573,3151],{"className":3152,"style":799},[798],[573,3154,3156],{"className":3155},[803,804,805,806],[573,3157,594],{"className":3158},[616,617,806],[573,3160],{"className":3161,"style":839},[748],[573,3163,2995],{"className":3164},[767],[573,3166],{"className":3167,"style":839},[748],[573,3169,700],{"className":3170},[616,617]," auf ",[573,3173,3175,3210],{"className":3174},[576],[573,3176,3178],{"className":3177},[580],[582,3179,3180],{"xmlns":584},[586,3181,3182,3207],{},[589,3183,3184,3186,3188,3190,3192,3194,3196,3198,3200,3202,3205],{},[669,3185,1078],{"stretchy":671},[2520,3187,2522],{},[669,3189,703],{"separator":603},[2520,3191,2525],{},[669,3193,1087],{"stretchy":671},[669,3195,1090],{},[669,3197,672],{"stretchy":671},[2520,3199,2522],{},[669,3201,703],{"separator":603},[592,3203,3204],{"mathvariant":956},"∞",[669,3206,677],{"stretchy":671},[596,3208,3209],{"encoding":598},"[0, 1] \\times (0, \\infty)",[573,3211,3213,3246],{"className":3212,"ariaHidden":603},[602],[573,3214,3216,3219,3222,3225,3228,3231,3234,3237,3240,3243],{"className":3215},[607],[573,3217],{"className":3218,"style":729},[611],[573,3220,1078],{"className":3221},[737],[573,3223,2522],{"className":3224},[616],[573,3226,703],{"className":3227},[853],[573,3229],{"className":3230,"style":839},[748],[573,3232,2525],{"className":3233},[616],[573,3235,1087],{"className":3236},[744],[573,3238],{"className":3239,"style":1127},[748],[573,3241,1090],{"className":3242},[1131],[573,3244],{"className":3245,"style":1127},[748],[573,3247,3249,3252,3255,3258,3261,3264,3267],{"className":3248},[607],[573,3250],{"className":3251,"style":729},[611],[573,3253,672],{"className":3254},[737],[573,3256,2522],{"className":3257},[616],[573,3259,703],{"className":3260},[853],[573,3262],{"className":3263,"style":839},[748],[573,3265,3204],{"className":3266},[616],[573,3268,677],{"className":3269},[744]," stetig (mit dem Wert ",[573,3272,3274,3287],{"className":3273},[576],[573,3275,3277],{"className":3276},[580],[582,3278,3279],{"xmlns":584},[586,3280,3281,3285],{},[589,3282,3283],{},[2520,3284,2522],{},[596,3286,2522],{"encoding":598},[573,3288,3290],{"className":3289,"ariaHidden":603},[602],[573,3291,3293,3296],{"className":3292},[607],[573,3294],{"className":3295,"style":2893},[611],[573,3297,2522],{"className":3298},[616]," bei ",[573,3301,3303,3321],{"className":3302},[576],[573,3304,3306],{"className":3305},[580],[582,3307,3308],{"xmlns":584},[586,3309,3310,3318],{},[589,3311,3312,3314,3316],{},[592,3313,700],{},[669,3315,680],{},[2520,3317,2522],{},[596,3319,3320],{"encoding":598},"x = 0",[573,3322,3324,3343],{"className":3323,"ariaHidden":603},[602],[573,3325,3327,3331,3334,3337,3340],{"className":3326},[607],[573,3328],{"className":3329,"style":3330},[611],"height:0.4306em;",[573,3332,700],{"className":3333},[616,617],[573,3335],{"className":3336,"style":749},[748],[573,3338,680],{"className":3339},[753],[573,3341],{"className":3342,"style":749},[748],[573,3344,3346,3349],{"className":3345},[607],[573,3347],{"className":3348,"style":2893},[611],[573,3350,2522],{"className":3351},[616],"), die Regel ist also direkt anwendbar. Für ",[573,3354,3356,3375],{"className":3355},[576],[573,3357,3359],{"className":3358},[580],[582,3360,3361],{"xmlns":584},[586,3362,3363,3373],{},[589,3364,3365,3367,3369,3371],{},[592,3366,594],{},[669,3368,2802],{},[669,3370,1756],{},[2520,3372,2525],{},[596,3374,2809],{"encoding":598},[573,3376,3378,3396],{"className":3377,"ariaHidden":603},[602],[573,3379,3381,3384,3387,3390,3393],{"className":3380},[607],[573,3382],{"className":3383,"style":1211},[611],[573,3385,594],{"className":3386},[616,617],[573,3388],{"className":3389,"style":749},[748],[573,3391,2802],{"className":3392},[753],[573,3394],{"className":3395,"style":749},[748],[573,3397,3399,3402,3405],{"className":3398},[607],[573,3400],{"className":3401,"style":2837},[611],[573,3403,1756],{"className":3404},[616],[573,3406,2525],{"className":3407},[616]," gilt das Ergebnis ebenfalls, dann mit der Majorante ",[573,3410,3412,3447],{"className":3411},[576],[573,3413,3415],{"className":3414},[580],[582,3416,3417],{"xmlns":584},[586,3418,3419,3444],{},[589,3420,3421,3432,3434,3436,3438,3440,3442],{},[1740,3422,3423,3425],{},[592,3424,700],{},[3426,3427,3428,3430],"msub",{},[592,3429,594],{},[2520,3431,2522],{},[709,3433,711],{},[592,3435,1296],{"mathvariant":956},[592,3437,2995],{},[669,3439,2998],{},[592,3441,700],{},[592,3443,1296],{"mathvariant":956},[596,3445,3446],{"encoding":598},"x^{t_0}\\,|\\ln x|",[573,3448,3450],{"className":3449,"ariaHidden":603},[602],[573,3451,3453,3457,3531,3534,3537,3540,3543,3546,3549],{"className":3452},[607],[573,3454],{"className":3455,"style":3456},[611],"height:1.0436em;vertical-align:-0.25em;",[573,3458,3460,3463],{"className":3459},[616],[573,3461,700],{"className":3462},[616,617],[573,3464,3466],{"className":3465},[777],[573,3467,3469],{"className":3468},[781],[573,3470,3472],{"className":3471},[786],[573,3473,3475],{"className":3474,"style":2670},[790],[573,3476,3477,3480],{"style":2673},[573,3478],{"className":3479,"style":799},[798],[573,3481,3483],{"className":3482},[803,804,805,806],[573,3484,3486],{"className":3485},[616,806],[573,3487,3489,3492],{"className":3488},[616,806],[573,3490,594],{"className":3491},[616,617,806],[573,3493,3495],{"className":3494},[777],[573,3496,3498,3522],{"className":3497},[781,782],[573,3499,3501,3519],{"className":3500},[786],[573,3502,3505],{"className":3503,"style":3504},[790],"height:0.3173em;",[573,3506,3508,3512],{"style":3507},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[573,3509],{"className":3510,"style":3511},[798],"height:2.5em;",[573,3513,3516],{"className":3514},[803,3515,2066,806],"reset-size3",[573,3517,2522],{"className":3518},[616,806],[573,3520,826],{"className":3521},[825],[573,3523,3525],{"className":3524},[786],[573,3526,3529],{"className":3527,"style":3528},[790],"height:0.143em;",[573,3530],{},[573,3532],{"className":3533,"style":839},[748],[573,3535,1296],{"className":3536},[616],[573,3538],{"className":3539,"style":839},[748],[573,3541,2995],{"className":3542},[767],[573,3544],{"className":3545,"style":839},[748],[573,3547,700],{"className":3548},[616,617],[573,3550,1296],{"className":3551},[616],[573,3553,3555,3584],{"className":3554},[576],[573,3556,3558],{"className":3557},[580],[582,3559,3560],{"xmlns":584},[586,3561,3562,3581],{},[589,3563,3564,3566,3569,3575,3577,3579],{},[592,3565,594],{},[669,3567,3568],{},"≥",[3426,3570,3571,3573],{},[592,3572,594],{},[2520,3574,2522],{},[669,3576,2802],{},[669,3578,1756],{},[2520,3580,2525],{},[596,3582,3583],{"encoding":598},"t \\geq t_0 > -1",[573,3585,3587,3606,3665],{"className":3586,"ariaHidden":603},[602],[573,3588,3590,3594,3597,3600,3603],{"className":3589},[607],[573,3591],{"className":3592,"style":3593},[611],"height:0.7719em;vertical-align:-0.136em;",[573,3595,594],{"className":3596},[616,617],[573,3598],{"className":3599,"style":749},[748],[573,3601,3568],{"className":3602},[753],[573,3604],{"className":3605,"style":749},[748],[573,3607,3609,3613,3656,3659,3662],{"className":3608},[607],[573,3610],{"className":3611,"style":3612},[611],"height:0.7651em;vertical-align:-0.15em;",[573,3614,3616,3619],{"className":3615},[616],[573,3617,594],{"className":3618},[616,617],[573,3620,3622],{"className":3621},[777],[573,3623,3625,3647],{"className":3624},[781,782],[573,3626,3628,3644],{"className":3627},[786],[573,3629,3632],{"className":3630,"style":3631},[790],"height:0.3011em;",[573,3633,3635,3638],{"style":3634},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[573,3636],{"className":3637,"style":799},[798],[573,3639,3641],{"className":3640},[803,804,805,806],[573,3642,2522],{"className":3643},[616,806],[573,3645,826],{"className":3646},[825],[573,3648,3650],{"className":3649},[786],[573,3651,3654],{"className":3652,"style":3653},[790],"height:0.15em;",[573,3655],{},[573,3657],{"className":3658,"style":749},[748],[573,3660,2802],{"className":3661},[753],[573,3663],{"className":3664,"style":749},[748],[573,3666,3668,3671,3674],{"className":3667},[607],[573,3669],{"className":3670,"style":2837},[611],[573,3672,1756],{"className":3673},[616],[573,3675,2525],{"className":3676},[616],". Ableiten nach 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x^t \\ln x\\,dx = F'(t) = -\\frac{1}{(t + 1)^2}",[573,3790,3792,3914,3971],{"className":3791,"ariaHidden":603},[602],[573,3793,3795,3799,3851,3854,3884,3887,3890,3893,3896,3899,3902,3905,3908,3911],{"className":3794},[607],[573,3796],{"className":3797,"style":3798},[611],"height:2.476em;vertical-align:-0.9119em;",[573,3800,3802,3805],{"className":3801},[767],[573,3803,686],{"className":3804,"style":773},[767,771,772],[573,3806,3808],{"className":3807},[777],[573,3809,3811,3843],{"className":3810},[781,782],[573,3812,3814,3840],{"className":3813},[786],[573,3815,3818,3829],{"className":3816,"style":3817},[790],"height:1.564em;",[573,3819,3820,3823],{"style":794},[573,3821],{"className":3822,"style":799},[798],[573,3824,3826],{"className":3825},[803,804,805,806],[573,3827,2522],{"className":3828},[616,806],[573,3830,3831,3834],{"style":812},[573,3832],{"className":3833,"style":799},[798],[573,3835,3837],{"className":3836},[803,804,805,806],[573,3838,2525],{"className":3839},[616,806],[573,3841,826],{"className":3842},[825],[573,3844,3846],{"className":3845},[786],[573,3847,3849],{"className":3848,"style":833},[790],[573,3850],{},[573,3852],{"className":3853,"style":839},[748],[573,3855,3857,3860],{"className":3856},[616],[573,3858,700],{"className":3859},[616,617],[573,3861,3863],{"className":3862},[777],[573,3864,3866],{"className":3865},[781],[573,3867,3869],{"className":3868},[786],[573,3870,3873],{"className":3871,"style":3872},[790],"height:0.8436em;",[573,3874,3875,3878],{"style":2118},[573,3876],{"className":3877,"style":799},[798],[573,3879,3881],{"className":3880},[803,804,805,806],[573,3882,594],{"className":3883},[616,617,806],[573,3885],{"className":3886,"style":839},[748],[573,3888,2995],{"className":3889},[767],[573,3891],{"className":3892,"style":839},[748],[573,3894,700],{"className":3895},[616,617],[573,3897],{"className":3898,"style":839},[748],[573,3900,714],{"className":3901},[616,617],[573,3903,700],{"className":3904},[616,617],[573,3906],{"className":3907,"style":749},[748],[573,3909,680],{"className":3910},[753],[573,3912],{"className":3913,"style":749},[748],[573,3915,3917,3921,3953,3956,3959,3962,3965,3968],{"className":3916},[607],[573,3918],{"className":3919,"style":3920},[611],"height:1.0519em;vertical-align:-0.25em;",[573,3922,3924,3927],{"className":3923},[616],[573,3925,667],{"className":3926,"style":733},[616,617],[573,3928,3930],{"className":3929},[777],[573,3931,3933],{"className":3932},[781],[573,3934,3936],{"className":3935},[786],[573,3937,3939],{"className":3938,"style":2115},[790],[573,3940,3941,3944],{"style":2118},[573,3942],{"className":3943,"style":799},[798],[573,3945,3947],{"className":3946},[803,804,805,806],[573,3948,3950],{"className":3949},[616,806],[573,3951,1747],{"className":3952},[616,806],[573,3954,672],{"className":3955},[737],[573,3957,594],{"className":3958},[616,617],[573,3960,677],{"className":3961},[744],[573,3963],{"className":3964,"style":749},[748],[573,3966,680],{"className":3967},[753],[573,3969],{"className":3970,"style":749},[748],[573,3972,3974,3978,3981],{"className":3973},[607],[573,3975],{"className":3976,"style":3977},[611],"height:2.2574em;vertical-align:-0.936em;",[573,3979,1756],{"className":3980},[616],[573,3982,3984,3987,4088],{"className":3983},[616],[573,3985],{"className":3986},[737,985],[573,3988,3990],{"className":3989},[950],[573,3991,3993,4079],{"className":3992},[781,782],[573,3994,3996,4076],{"className":3995},[786],[573,3997,4000,4057,4065],{"className":3998,"style":3999},[790],"height:1.3214em;",[573,4001,4002,4005],{"style":1880},[573,4003],{"className":4004,"style":1005},[798],[573,4006,4008,4011,4014,4017,4020,4023,4026],{"className":4007},[616],[573,4009,672],{"className":4010},[737],[573,4012,594],{"className":4013},[616,617],[573,4015],{"className":4016,"style":1127},[748],[573,4018,1791],{"className":4019},[1131],[573,4021],{"className":4022,"style":1127},[748],[573,4024,2525],{"className":4025},[616],[573,4027,4029,4032],{"className":4028},[744],[573,4030,677],{"className":4031},[744],[573,4033,4035],{"className":4034},[777],[573,4036,4038],{"className":4037},[781],[573,4039,4041],{"className":4040},[786],[573,4042,4045],{"className":4043,"style":4044},[790],"height:0.7401em;",[573,4046,4048,4051],{"style":4047},"top:-2.989em;margin-right:0.05em;",[573,4049],{"className":4050,"style":799},[798],[573,4052,4054],{"className":4053},[803,804,805,806],[573,4055,3785],{"className":4056},[616,806],[573,4058,4059,4062],{"style":1021},[573,4060],{"className":4061,"style":1005},[798],[573,4063],{"className":4064,"style":1029},[1028],[573,4066,4067,4070],{"style":1903},[573,4068],{"className":4069,"style":1005},[798],[573,4071,4073],{"className":4072},[616],[573,4074,2525],{"className":4075},[616],[573,4077,826],{"className":4078},[825],[573,4080,4082],{"className":4081},[786],[573,4083,4086],{"className":4084,"style":4085},[790],"height:0.936em;",[573,4087],{},[573,4089],{"className":4090},[744,985],[564,4092,4093,4094,4145,4146,4399],{},"Für 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",[573,4147,4149,4198],{"className":4148},[576],[573,4150,4152],{"className":4151},[580],[582,4153,4154],{"xmlns":584},[586,4155,4156,4195],{},[589,4157,4158,4166,4172,4174,4176,4178,4180,4182,4184,4186,4188],{},[682,4159,4160,4162,4164],{},[669,4161,686],{},[2520,4163,2522],{},[2520,4165,2525],{},[1740,4167,4168,4170],{},[592,4169,700],{},[2520,4171,3785],{},[592,4173,2995],{},[669,4175,2998],{},[592,4177,700],{},[709,4179,711],{},[592,4181,714],{},[592,4183,700],{},[669,4185,680],{},[669,4187,1756],{},[950,4189,4190,4192],{},[2520,4191,2525],{},[2520,4193,4194],{},"9",[596,4196,4197],{"encoding":598},"\\int_0^1 x^2 \\ln x\\,dx = -\\frac{1}{9}",[573,4199,4201,4321],{"className":4200,"ariaHidden":603},[602],[573,4202,4204,4207,4258,4261,4291,4294,4297,4300,4303,4306,4309,4312,4315,4318],{"className":4203},[607],[573,4205],{"className":4206,"style":2591},[611],[573,4208,4210,4213],{"className":4209},[767],[573,4211,686],{"className":4212,"style":2599},[767,771,2598],[573,4214,4216],{"className":4215},[777],[573,4217,4219,4250],{"className":4218},[781,782],[573,4220,4222,4247],{"className":4221},[786],[573,4223,4225,4236],{"className":4224,"style":2612},[790],[573,4226,4227,4230],{"style":2615},[573,4228],{"className":4229,"style":799},[798],[573,4231,4233],{"className":4232},[803,804,805,806],[573,4234,2522],{"className":4235},[616,806],[573,4237,4238,4241],{"style":2627},[573,4239],{"className":4240,"style":799},[798],[573,4242,4244],{"className":4243},[803,804,805,806],[573,4245,2525],{"className":4246},[616,806],[573,4248,826],{"className":4249},[825],[573,4251,4253],{"className":4252},[786],[573,4254,4256],{"className":4255,"style":2646},[790],[573,4257],{},[573,4259],{"className":4260,"style":839},[748],[573,4262,4264,4267],{"className":4263},[616],[573,4265,700],{"className":4266},[616,617],[573,4268,4270],{"className":4269},[777],[573,4271,4273],{"className":4272},[781],[573,4274,4276],{"className":4275},[786],[573,4277,4280],{"className":4278,"style":4279},[790],"height:0.8141em;",[573,4281,4282,4285],{"style":2673},[573,4283],{"className":4284,"style":799},[798],[573,4286,4288],{"className":4287},[803,804,805,806],[573,4289,3785],{"className":4290},[616,806],[573,4292],{"className":4293,"style":839},[748],[573,4295,2995],{"className":4296},[767],[573,4298],{"className":4299,"style":839},[748],[573,4301,700],{"className":4302},[616,617],[573,4304],{"className":4305,"style":839},[748],[573,4307,714],{"className":4308},[616,617],[573,4310,700],{"className":4311},[616,617],[573,4313],{"className":4314,"style":749},[748],[573,4316,680],{"className":4317},[753],[573,4319],{"className":4320,"style":749},[748],[573,4322,4324,4328,4331],{"className":4323},[607],[573,4325],{"className":4326,"style":4327},[611],"height:1.1901em;vertical-align:-0.345em;",[573,4329,1756],{"className":4330},[616],[573,4332,4334,4337,4396],{"className":4333},[616],[573,4335],{"className":4336},[737,985],[573,4338,4340],{"className":4339},[950],[573,4341,4343,4388],{"className":4342},[781,782],[573,4344,4346,4385],{"className":4345},[786],[573,4347,4349,4363,4371],{"className":4348,"style":2726},[790],[573,4350,4351,4354],{"style":1001},[573,4352],{"className":4353,"style":1005},[798],[573,4355,4357],{"className":4356},[803,804,805,806],[573,4358,4360],{"className":4359},[616,806],[573,4361,4194],{"className":4362},[616,806],[573,4364,4365,4368],{"style":1021},[573,4366],{"className":4367,"style":1005},[798],[573,4369],{"className":4370,"style":1029},[1028],[573,4372,4373,4376],{"style":2757},[573,4374],{"className":4375,"style":1005},[798],[573,4377,4379],{"className":4378},[803,804,805,806],[573,4380,4382],{"className":4381},[616,806],[573,4383,2525],{"className":4384},[616,806],[573,4386,826],{"className":4387},[825],[573,4389,4391],{"className":4390},[786],[573,4392,4394],{"className":4393,"style":1057},[790],[573,4395],{},[573,4397],{"className":4398},[744,985],".",[564,4401,4402,4403,4559],{},"Variable Grenze: ",[573,4404,4406,4449],{"className":4405},[576],[573,4407,4409],{"className":4408},[580],[582,4410,4411],{"xmlns":584},[586,4412,4413,4446],{},[589,4414,4415,4418,4420,4422,4424,4426,4434,4436,4438,4440,4442,4444],{},[592,4416,4417],{},"G",[669,4419,672],{"stretchy":671},[592,4421,594],{},[669,4423,677],{"stretchy":671},[669,4425,680],{},[682,4427,4428,4430,4432],{},[669,4429,686],{},[2520,4431,2522],{},[592,4433,594],{},[592,4435,700],{},[709,4437,711],{},[592,4439,594],{},[709,4441,711],{},[592,4443,714],{},[592,4445,700],{},[596,4447,4448],{"encoding":598},"G(t) = \\int_0^t x\\,t\\,dx",[573,4450,4452,4479],{"className":4451,"ariaHidden":603},[602],[573,4453,4455,4458,4461,4464,4467,4470,4473,4476],{"className":4454},[607],[573,4456],{"className":4457,"style":729},[611],[573,4459,4417],{"className":4460},[616,617],[573,4462,672],{"className":4463},[737],[573,4465,594],{"className":4466},[616,617],[573,4468,677],{"className":4469},[744],[573,4471],{"className":4472,"style":749},[748],[573,4474,680],{"className":4475},[753],[573,4477],{"className":4478,"style":749},[748],[573,4480,4482,4486,4538,4541,4544,4547,4550,4553,4556],{"className":4481},[607],[573,4483],{"className":4484,"style":4485},[611],"height:1.3443em;vertical-align:-0.3558em;",[573,4487,4489,4492],{"className":4488},[767],[573,4490,686],{"className":4491,"style":2599},[767,771,2598],[573,4493,4495],{"className":4494},[777],[573,4496,4498,4530],{"className":4497},[781,782],[573,4499,4501,4527],{"className":4500},[786],[573,4502,4505,4516],{"className":4503,"style":4504},[790],"height:0.9885em;",[573,4506,4507,4510],{"style":2615},[573,4508],{"className":4509,"style":799},[798],[573,4511,4513],{"className":4512},[803,804,805,806],[573,4514,2522],{"className":4515},[616,806],[573,4517,4518,4521],{"style":2627},[573,4519],{"className":4520,"style":799},[798],[573,4522,4524],{"className":4523},[803,804,805,806],[573,4525,594],{"className":4526},[616,617,806],[573,4528,826],{"className":4529},[825],[573,4531,4533],{"className":4532},[786],[573,4534,4536],{"className":4535,"style":2646},[790],[573,4537],{},[573,4539],{"className":4540,"style":839},[748],[573,4542,700],{"className":4543},[616,617],[573,4545],{"className":4546,"style":839},[748],[573,4548,594],{"className":4549},[616,617],[573,4551],{"className":4552,"style":839},[748],[573,4554,714],{"className":4555},[616,617],[573,4557,700],{"className":4558},[616,617],". Mit der erweiterten Regel:",[573,4561,4563],{"className":4562},[651],[573,4564,4566,4656],{"className":4565},[576],[573,4567,4569],{"className":4568},[580],[582,4570,4571],{"xmlns":584,"display":660},[586,4572,4573,4653],{},[589,4574,4575,4581,4583,4585,4587,4589,4591,4594,4596,4598,4600,4602,4610,4612,4614,4616,4618,4620,4626,4628,4638,4640,4647],{},[1740,4576,4577,4579],{},[592,4578,4417],{},[669,4580,1747],{"mathvariant":956,"lspace":1746,"rspace":1746},[669,4582,672],{"stretchy":671},[592,4584,594],{},[669,4586,677],{"stretchy":671},[669,4588,680],{},[592,4590,594],{},[669,4592,4593],{},"⋅",[592,4595,594],{},[669,4597,4593],{},[2520,4599,2525],{},[669,4601,1791],{},[682,4603,4604,4606,4608],{},[669,4605,686],{},[2520,4607,2522],{},[592,4609,594],{},[592,4611,700],{},[709,4613,711],{},[592,4615,714],{},[592,4617,700],{},[669,4619,680],{},[1740,4621,4622,4624],{},[592,4623,594],{},[2520,4625,3785],{},[669,4627,1791],{},[950,4629,4630,4636],{},[1740,4631,4632,4634],{},[592,4633,594],{},[2520,4635,3785],{},[2520,4637,3785],{},[669,4639,680],{},[950,4641,4642,4645],{},[2520,4643,4644],{},"3",[2520,4646,3785],{},[1740,4648,4649,4651],{},[592,4650,594],{},[2520,4652,3785],{},[596,4654,4655],{"encoding":598},"G'(t) = t \\cdot t \\cdot 1 + \\int_0^t x\\,dx = t^2 + \\frac{t^2}{2} = \\frac{3}{2}t^2",[573,4657,4659,4715,4733,4751,4769,4852,4898,5003],{"className":4658,"ariaHidden":603},[602],[573,4660,4662,4665,4697,4700,4703,4706,4709,4712],{"className":4661},[607],[573,4663],{"className":4664,"style":3920},[611],[573,4666,4668,4671],{"className":4667},[616],[573,4669,4417],{"className":4670},[616,617],[573,4672,4674],{"className":4673},[777],[573,4675,4677],{"className":4676},[781],[573,4678,4680],{"className":4679},[786],[573,4681,4683],{"className":4682,"style":2115},[790],[573,4684,4685,4688],{"style":2118},[573,4686],{"className":4687,"style":799},[798],[573,4689,4691],{"className":4690},[803,804,805,806],[573,4692,4694],{"className":4693},[616,806],[573,4695,1747],{"className":4696},[616,806],[573,4698,672],{"className":4699},[737],[573,4701,594],{"className":4702},[616,617],[573,4704,677],{"className":4705},[744],[573,4707],{"className":4708,"style":749},[748],[573,4710,680],{"className":4711},[753],[573,4713],{"className":4714,"style":749},[748],[573,4716,4718,4721,4724,4727,4730],{"className":4717},[607],[573,4719],{"className":4720,"style":612},[611],[573,4722,594],{"className":4723},[616,617],[573,4725],{"className":4726,"style":1127},[748],[573,4728,4593],{"className":4729},[1131],[573,4731],{"className":4732,"style":1127},[748],[573,4734,4736,4739,4742,4745,4748],{"className":4735},[607],[573,4737],{"className":4738,"style":612},[611],[573,4740,594],{"className":4741},[616,617],[573,4743],{"className":4744,"style":1127},[748],[573,4746,4593],{"className":4747},[1131],[573,4749],{"className":4750,"style":1127},[748],[573,4752,4754,4757,4760,4763,4766],{"className":4753},[607],[573,4755],{"className":4756,"style":2837},[611],[573,4758,2525],{"className":4759},[616],[573,4761],{"className":4762,"style":1127},[748],[573,4764,1791],{"className":4765},[1131],[573,4767],{"className":4768,"style":1127},[748],[573,4770,4772,4776,4828,4831,4834,4837,4840,4843,4846,4849],{"className":4771},[607],[573,4773],{"className":4774,"style":4775},[611],"height:2.4554em;vertical-align:-0.9119em;",[573,4777,4779,4782],{"className":4778},[767],[573,4780,686],{"className":4781,"style":773},[767,771,772],[573,4783,4785],{"className":4784},[777],[573,4786,4788,4820],{"className":4787},[781,782],[573,4789,4791,4817],{"className":4790},[786],[573,4792,4795,4806],{"className":4793,"style":4794},[790],"height:1.5435em;",[573,4796,4797,4800],{"style":794},[573,4798],{"className":4799,"style":799},[798],[573,4801,4803],{"className":4802},[803,804,805,806],[573,4804,2522],{"className":4805},[616,806],[573,4807,4808,4811],{"style":812},[573,4809],{"className":4810,"style":799},[798],[573,4812,4814],{"className":4813},[803,804,805,806],[573,4815,594],{"className":4816},[616,617,806],[573,4818,826],{"className":4819},[825],[573,4821,4823],{"className":4822},[786],[573,4824,4826],{"className":4825,"style":833},[790],[573,4827],{},[573,4829],{"className":4830,"style":839},[748],[573,4832,700],{"className":4833},[616,617],[573,4835],{"className":4836,"style":839},[748],[573,4838,714],{"className":4839},[616,617],[573,4841,700],{"className":4842},[616,617],[573,4844],{"className":4845,"style":749},[748],[573,4847,680],{"className":4848},[753],[573,4850],{"className":4851,"style":749},[748],[573,4853,4855,4859,4889,4892,4895],{"className":4854},[607],[573,4856],{"className":4857,"style":4858},[611],"height:0.9474em;vertical-align:-0.0833em;",[573,4860,4862,4865],{"className":4861},[616],[573,4863,594],{"className":4864},[616,617],[573,4866,4868],{"className":4867},[777],[573,4869,4871],{"className":4870},[781],[573,4872,4874],{"className":4873},[786],[573,4875,4878],{"className":4876,"style":4877},[790],"height:0.8641em;",[573,4879,4880,4883],{"style":2118},[573,4881],{"className":4882,"style":799},[798],[573,4884,4886],{"className":4885},[803,804,805,806],[573,4887,3785],{"className":4888},[616,806],[573,4890],{"className":4891,"style":1127},[748],[573,4893,1791],{"className":4894},[1131],[573,4896],{"className":4897,"style":1127},[748],[573,4899,4901,4905,4994,4997,5000],{"className":4900},[607],[573,4902],{"className":4903,"style":4904},[611],"height:2.1771em;vertical-align:-0.686em;",[573,4906,4908,4911,4991],{"className":4907},[616],[573,4909],{"className":4910},[737,985],[573,4912,4914],{"className":4913},[950],[573,4915,4917,4983],{"className":4916},[781,782],[573,4918,4920,4980],{"className":4919},[786],[573,4921,4924,4935,4943],{"className":4922,"style":4923},[790],"height:1.4911em;",[573,4925,4926,4929],{"style":1880},[573,4927],{"className":4928,"style":1005},[798],[573,4930,4932],{"className":4931},[616],[573,4933,3785],{"className":4934},[616],[573,4936,4937,4940],{"style":1021},[573,4938],{"className":4939,"style":1005},[798],[573,4941],{"className":4942,"style":1029},[1028],[573,4944,4945,4948],{"style":1903},[573,4946],{"className":4947,"style":1005},[798],[573,4949,4951],{"className":4950},[616],[573,4952,4954,4957],{"className":4953},[616],[573,4955,594],{"className":4956},[616,617],[573,4958,4960],{"className":4959},[777],[573,4961,4963],{"className":4962},[781],[573,4964,4966],{"className":4965},[786],[573,4967,4969],{"className":4968,"style":4279},[790],[573,4970,4971,4974],{"style":2673},[573,4972],{"className":4973,"style":799},[798],[573,4975,4977],{"className":4976},[803,804,805,806],[573,4978,3785],{"className":4979},[616,806],[573,4981,826],{"className":4982},[825],[573,4984,4986],{"className":4985},[786],[573,4987,4989],{"className":4988,"style":1922},[790],[573,4990],{},[573,4992],{"className":4993},[744,985],[573,4995],{"className":4996,"style":749},[748],[573,4998,680],{"className":4999},[753],[573,5001],{"className":5002,"style":749},[748],[573,5004,5006,5010,5072],{"className":5005},[607],[573,5007],{"className":5008,"style":5009},[611],"height:2.0074em;vertical-align:-0.686em;",[573,5011,5013,5016,5069],{"className":5012},[616],[573,5014],{"className":5015},[737,985],[573,5017,5019],{"className":5018},[950],[573,5020,5022,5061],{"className":5021},[781,782],[573,5023,5025,5058],{"className":5024},[786],[573,5026,5028,5039,5047],{"className":5027,"style":3999},[790],[573,5029,5030,5033],{"style":1880},[573,5031],{"className":5032,"style":1005},[798],[573,5034,5036],{"className":5035},[616],[573,5037,3785],{"className":5038},[616],[573,5040,5041,5044],{"style":1021},[573,5042],{"className":5043,"style":1005},[798],[573,5045],{"className":5046,"style":1029},[1028],[573,5048,5049,5052],{"style":1903},[573,5050],{"className":5051,"style":1005},[798],[573,5053,5055],{"className":5054},[616],[573,5056,4644],{"className":5057},[616],[573,5059,826],{"className":5060},[825],[573,5062,5064],{"className":5063},[786],[573,5065,5067],{"className":5066,"style":1922},[790],[573,5068],{},[573,5070],{"className":5071},[744,985],[573,5073,5075,5078],{"className":5074},[616],[573,5076,594],{"className":5077},[616,617],[573,5079,5081],{"className":5080},[777],[573,5082,5084],{"className":5083},[781],[573,5085,5087],{"className":5086},[786],[573,5088,5090],{"className":5089,"style":4877},[790],[573,5091,5092,5095],{"style":2118},[573,5093],{"className":5094,"style":799},[798],[573,5096,5098],{"className":5097},[803,804,805,806],[573,5099,3785],{"className":5100},[616,806],[564,5102,5103,5104,5416,5417,4399],{},"Zur Kontrolle: Direkt ist ",[573,5105,5107,5155],{"className":5106},[576],[573,5108,5110],{"className":5109},[580],[582,5111,5112],{"xmlns":584},[586,5113,5114,5152],{},[589,5115,5116,5118,5120,5122,5124,5126,5128,5130,5140,5142],{},[592,5117,4417],{},[669,5119,672],{"stretchy":671},[592,5121,594],{},[669,5123,677],{"stretchy":671},[669,5125,680],{},[592,5127,594],{},[669,5129,4593],{},[950,5131,5132,5138],{},[1740,5133,5134,5136],{},[592,5135,594],{},[2520,5137,3785],{},[2520,5139,3785],{},[669,5141,680],{},[950,5143,5144,5150],{},[1740,5145,5146,5148],{},[592,5147,594],{},[2520,5149,4644],{},[2520,5151,3785],{},[596,5153,5154],{"encoding":598},"G(t) = t \\cdot \\frac{t^2}{2} = \\frac{t^3}{2}",[573,5156,5158,5185,5203,5316],{"className":5157,"ariaHidden":603},[602],[573,5159,5161,5164,5167,5170,5173,5176,5179,5182],{"className":5160},[607],[573,5162],{"className":5163,"style":729},[611],[573,5165,4417],{"className":5166},[616,617],[573,5168,672],{"className":5169},[737],[573,5171,594],{"className":5172},[616,617],[573,5174,677],{"className":5175},[744],[573,5177],{"className":5178,"style":749},[748],[573,5180,680],{"className":5181},[753],[573,5183],{"className":5184,"style":749},[748],[573,5186,5188,5191,5194,5197,5200],{"className":5187},[607],[573,5189],{"className":5190,"style":612},[611],[573,5192,594],{"className":5193},[616,617],[573,5195],{"className":5196,"style":1127},[748],[573,5198,4593],{"className":5199},[1131],[573,5201],{"className":5202,"style":1127},[748],[573,5204,5206,5210,5307,5310,5313],{"className":5205},[607],[573,5207],{"className":5208,"style":5209},[611],"height:1.3629em;vertical-align:-0.345em;",[573,5211,5213,5216,5304],{"className":5212},[616],[573,5214],{"className":5215},[737,985],[573,5217,5219],{"className":5218},[950],[573,5220,5222,5296],{"className":5221},[781,782],[573,5223,5225,5293],{"className":5224},[786],[573,5226,5229,5243,5251],{"className":5227,"style":5228},[790],"height:1.0179em;",[573,5230,5231,5234],{"style":1001},[573,5232],{"className":5233,"style":1005},[798],[573,5235,5237],{"className":5236},[803,804,805,806],[573,5238,5240],{"className":5239},[616,806],[573,5241,3785],{"className":5242},[616,806],[573,5244,5245,5248],{"style":1021},[573,5246],{"className":5247,"style":1005},[798],[573,5249],{"className":5250,"style":1029},[1028],[573,5252,5253,5256],{"style":2757},[573,5254],{"className":5255,"style":1005},[798],[573,5257,5259],{"className":5258},[803,804,805,806],[573,5260,5262],{"className":5261},[616,806],[573,5263,5265,5268],{"className":5264},[616,806],[573,5266,594],{"className":5267},[616,617,806],[573,5269,5271],{"className":5270},[777],[573,5272,5274],{"className":5273},[781],[573,5275,5277],{"className":5276},[786],[573,5278,5281],{"className":5279,"style":5280},[790],"height:0.8913em;",[573,5282,5284,5287],{"style":5283},"top:-2.931em;margin-right:0.0714em;",[573,5285],{"className":5286,"style":3511},[798],[573,5288,5290],{"className":5289},[803,3515,2066,806],[573,5291,3785],{"className":5292},[616,806],[573,5294,826],{"className":5295},[825],[573,5297,5299],{"className":5298},[786],[573,5300,5302],{"className":5301,"style":1057},[790],[573,5303],{},[573,5305],{"className":5306},[744,985],[573,5308],{"className":5309,"style":749},[748],[573,5311,680],{"className":5312},[753],[573,5314],{"className":5315,"style":749},[748],[573,5317,5319,5322],{"className":5318},[607],[573,5320],{"className":5321,"style":5209},[611],[573,5323,5325,5328,5413],{"className":5324},[616],[573,5326],{"className":5327},[737,985],[573,5329,5331],{"className":5330},[950],[573,5332,5334,5405],{"className":5333},[781,782],[573,5335,5337,5402],{"className":5336},[786],[573,5338,5340,5354,5362],{"className":5339,"style":5228},[790],[573,5341,5342,5345],{"style":1001},[573,5343],{"className":5344,"style":1005},[798],[573,5346,5348],{"className":5347},[803,804,805,806],[573,5349,5351],{"className":5350},[616,806],[573,5352,3785],{"className":5353},[616,806],[573,5355,5356,5359],{"style":1021},[573,5357],{"className":5358,"style":1005},[798],[573,5360],{"className":5361,"style":1029},[1028],[573,5363,5364,5367],{"style":2757},[573,5365],{"className":5366,"style":1005},[798],[573,5368,5370],{"className":5369},[803,804,805,806],[573,5371,5373],{"className":5372},[616,806],[573,5374,5376,5379],{"className":5375},[616,806],[573,5377,594],{"className":5378},[616,617,806],[573,5380,5382],{"className":5381},[777],[573,5383,5385],{"className":5384},[781],[573,5386,5388],{"className":5387},[786],[573,5389,5391],{"className":5390,"style":5280},[790],[573,5392,5393,5396],{"style":5283},[573,5394],{"className":5395,"style":3511},[798],[573,5397,5399],{"className":5398},[803,3515,2066,806],[573,5400,4644],{"className":5401},[616,806],[573,5403,826],{"className":5404},[825],[573,5406,5408],{"className":5407},[786],[573,5409,5411],{"className":5410,"style":1057},[790],[573,5412],{},[573,5414],{"className":5415},[744,985],", und die Ableitung ist ",[573,5418,5420,5444],{"className":5419},[576],[573,5421,5423],{"className":5422},[580],[582,5424,5425],{"xmlns":584},[586,5426,5427,5441],{},[589,5428,5429,5435],{},[950,5430,5431,5433],{},[2520,5432,4644],{},[2520,5434,3785],{},[1740,5436,5437,5439],{},[592,5438,594],{},[2520,5440,3785],{},[596,5442,5443],{"encoding":598},"\\frac{3}{2}t^2",[573,5445,5447],{"className":5446,"ariaHidden":603},[602],[573,5448,5450,5453,5521],{"className":5449},[607],[573,5451],{"className":5452,"style":4327},[611],[573,5454,5456,5459,5518],{"className":5455},[616],[573,5457],{"className":5458},[737,985],[573,5460,5462],{"className":5461},[950],[573,5463,5465,5510],{"className":5464},[781,782],[573,5466,5468,5507],{"className":5467},[786],[573,5469,5471,5485,5493],{"className":5470,"style":2726},[790],[573,5472,5473,5476],{"style":1001},[573,5474],{"className":5475,"style":1005},[798],[573,5477,5479],{"className":5478},[803,804,805,806],[573,5480,5482],{"className":5481},[616,806],[573,5483,3785],{"className":5484},[616,806],[573,5486,5487,5490],{"style":1021},[573,5488],{"className":5489,"style":1005},[798],[573,5491],{"className":5492,"style":1029},[1028],[573,5494,5495,5498],{"style":2757},[573,5496],{"className":5497,"style":1005},[798],[573,5499,5501],{"className":5500},[803,804,805,806],[573,5502,5504],{"className":5503},[616,806],[573,5505,4644],{"className":5506},[616,806],[573,5508,826],{"className":5509},[825],[573,5511,5513],{"className":5512},[786],[573,5514,5516],{"className":5515,"style":1057},[790],[573,5517],{},[573,5519],{"className":5520},[744,985],[573,5522,5524,5527],{"className":5523},[616],[573,5525,594],{"className":5526},[616,617],[573,5528,5530],{"className":5529},[777],[573,5531,5533],{"className":5532},[781],[573,5534,5536],{"className":5535},[786],[573,5537,5539],{"className":5538,"style":4279},[790],[573,5540,5541,5544],{"style":2673},[573,5542],{"className":5543,"style":799},[798],[573,5545,5547],{"className":5546},[803,804,805,806],[573,5548,3785],{"className":5549},[616,806],[559,5551,5553],{"id":5552},"typische-fehler","Typische Fehler",[5555,5556,5557,5690,5751],"ul",{},[5558,5559,5560,5561,5689],"li",{},"Bei variablen Grenzen die Randterme vergessen. Im zweiten Beispiel käme sonst nur ",[573,5562,5564,5586],{"className":5563},[576],[573,5565,5567],{"className":5566},[580],[582,5568,5569],{"xmlns":584},[586,5570,5571,5583],{},[589,5572,5573],{},[950,5574,5575,5581],{},[1740,5576,5577,5579],{},[592,5578,594],{},[2520,5580,3785],{},[2520,5582,3785],{},[596,5584,5585],{"encoding":598},"\\frac{t^2}{2}",[573,5587,5589],{"className":5588,"ariaHidden":603},[602],[573,5590,5592,5595],{"className":5591},[607],[573,5593],{"className":5594,"style":5209},[611],[573,5596,5598,5601,5686],{"className":5597},[616],[573,5599],{"className":5600},[737,985],[573,5602,5604],{"className":5603},[950],[573,5605,5607,5678],{"className":5606},[781,782],[573,5608,5610,5675],{"className":5609},[786],[573,5611,5613,5627,5635],{"className":5612,"style":5228},[790],[573,5614,5615,5618],{"style":1001},[573,5616],{"className":5617,"style":1005},[798],[573,5619,5621],{"className":5620},[803,804,805,806],[573,5622,5624],{"className":5623},[616,806],[573,5625,3785],{"className":5626},[616,806],[573,5628,5629,5632],{"style":1021},[573,5630],{"className":5631,"style":1005},[798],[573,5633],{"className":5634,"style":1029},[1028],[573,5636,5637,5640],{"style":2757},[573,5638],{"className":5639,"style":1005},[798],[573,5641,5643],{"className":5642},[803,804,805,806],[573,5644,5646],{"className":5645},[616,806],[573,5647,5649,5652],{"className":5648},[616,806],[573,5650,594],{"className":5651},[616,617,806],[573,5653,5655],{"className":5654},[777],[573,5656,5658],{"className":5657},[781],[573,5659,5661],{"className":5660},[786],[573,5662,5664],{"className":5663,"style":5280},[790],[573,5665,5666,5669],{"style":5283},[573,5667],{"className":5668,"style":3511},[798],[573,5670,5672],{"className":5671},[803,3515,2066,806],[573,5673,3785],{"className":5674},[616,806],[573,5676,826],{"className":5677},[825],[573,5679,5681],{"className":5680},[786],[573,5682,5684],{"className":5683,"style":1057},[790],[573,5685],{},[573,5687],{"className":5688},[744,985]," heraus.",[5558,5691,5692,5693,5721,5722,5750],{},"Nach der Integrationsvariablen ",[573,5694,5696,5709],{"className":5695},[576],[573,5697,5699],{"className":5698},[580],[582,5700,5701],{"xmlns":584},[586,5702,5703,5707],{},[589,5704,5705],{},[592,5706,700],{},[596,5708,700],{"encoding":598},[573,5710,5712],{"className":5711,"ariaHidden":603},[602],[573,5713,5715,5718],{"className":5714},[607],[573,5716],{"className":5717,"style":3330},[611],[573,5719,700],{"className":5720},[616,617]," statt nach dem Parameter ",[573,5723,5725,5738],{"className":5724},[576],[573,5726,5728],{"className":5727},[580],[582,5729,5730],{"xmlns":584},[586,5731,5732,5736],{},[589,5733,5734],{},[592,5735,594],{},[596,5737,594],{"encoding":598},[573,5739,5741],{"className":5740,"ariaHidden":603},[602],[573,5742,5744,5747],{"className":5743},[607],[573,5745],{"className":5746,"style":612},[611],[573,5748,594],{"className":5749},[616,617]," ableiten.",[5558,5752,5753],{},"Die Regel ohne Prüfung bei uneigentlichen Integralen anwenden. Ohne stetige Ableitung auf dem Rechteck oder integrierbare Majorante kann das Vertauschen ein falsches Ergebnis liefern.",{"title":5755,"searchDepth":5756,"depth":5756,"links":5757},"",2,[5758,5759,5760],{"id":561,"depth":5756,"text":562},{"id":2489,"depth":5756,"text":2490},{"id":5552,"depth":5756,"text":5553},[5762,5765,5768,5771,5773,5776],{"lhs":5763,"rhs":5764},"round(sum(map(0:999, f(k) = ((k + 0.5)\u002F1000)^2))\u002F1000, 4)","round(1\u002F3, 4)",{"lhs":5766,"rhs":5767},"round(sum(map(0:999, f(k) = ((k + 0.5)\u002F1000)^2 * log((k + 0.5)\u002F1000)))\u002F1000, 4)","round(-1\u002F9, 4)",{"lhs":5769,"rhs":5770},"-1\u002F(2 + 1)^2","-1\u002F9",{"lhs":5772,"rhs":2522},"round((1\u002F(t + 1e-5 + 1) - 1\u002F(t - 1e-5 + 1))\u002F2e-5 + 1\u002F(t + 1)^2, 6)",{"lhs":5774,"rhs":5775},"t*t*1 + t^2\u002F2","3*t^2\u002F2",{"lhs":5777,"rhs":2522},"round(((t + 1e-5)^3\u002F2 - (t - 1e-5)^3\u002F2)\u002F2e-5 - 3*t^2\u002F2, 6)","a, b \\text{ fest},\\ f \\text{ und } \\tfrac{\\partial f}{\\partial t} \\text{ stetig auf } [a, b] \\times I,\\ t \\in I \\text{ (offenes Intervall)}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">fest\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">und\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmfrac>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmi>t\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmstyle>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\tfrac{\\partial f}{\\partial t}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.2772em;vertical-align:-0.345em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9322em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">t\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.4461em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\" style=\"margin-right:0.0556em;\">∂\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">stetig auf\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003Cmo>×\u003C\u002Fmo>\u003Cmi>I\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">[a, b] \\times I,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">[\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">]\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">×\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">I\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>t\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi>I\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">t \\in I\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6542em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">I\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">(offenes Intervall)\u003C\u002Fspan>",null,"md","leibniz-integral-rule","\\frac{d}{dt} \\int_{a}^{b} f(x, t)\\,dx = \\int_{a}^{b} \\frac{\\partial f}{\\partial t}(x, t)\\,dx","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmfrac>\u003Cmi>d\u003C\u002Fmi>\u003Cmrow>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>t\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmsubsup>\u003Cmo>∫\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmsubsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>t\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsubsup>\u003Cmo>∫\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmsubsup>\u003Cmfrac>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∂\u003C\u002Fmi>\u003Cmi>t\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>t\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\frac{d}{dt} \\int_{a}^{b} f(x, t)\\,dx = \\int_{a}^{b} \\frac{\\partial f}{\\partial t}(x, t)\\,dx\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.511em;vertical-align:-0.9119em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.599em;\">\u003Cspan 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