3.1 Integrals 1 to 100

  3.1.1 \(\int \sin (x) \sin (2 x) \sin (3 x) \, dx\) [1]
  3.1.2 \(\int \cos (x) \sin ^3(2 x) \, dx\) [2]
  3.1.3 \(\int \sqrt [3]{-1+x} (1+x)^2 \, dx\) [3]
  3.1.4 \(\int x \log (1+\genfrac {}{}{}{}{1}{x}) \, dx\) [4]
  3.1.5 \(\int \sin ^2(\log (x)) \, dx\) [5]
  3.1.6 \(\int \genfrac {}{}{}{}{1}{1+3 e^x} \, dx\) [6]
  3.1.7 \(\int \csc ^3(x) \sec ^5(x) \, dx\) [7]
  3.1.8 \(\int \genfrac {}{}{}{}{1}{x \sqrt {-1+x^4}} \, dx\) [8]
  3.1.9 \(\int \genfrac {}{}{}{}{1}{x (1+x^5)} \, dx\) [9]
  3.1.10 \(\int \sqrt {\tan (x)} \, dx\) [10]
  3.1.11 \(\int \genfrac {}{}{}{}{\log (1+x)}{1+x^2} \, dx\) [11]
  3.1.12 \(\int \genfrac {}{}{}{}{\sqrt {x}}{-\sqrt [3]{x}+\sqrt {x}} \, dx\) [12]
  3.1.13 \(\int x^x (1+\log (x)) \, dx\) [13]
  3.1.14 \(\int x^{13/2} \sqrt {1+x^{5/2}} \, dx\) [14]
  3.1.15 \(\int \genfrac {}{}{}{}{1}{(1+x^2)^2} \, dx\) [15]
  3.1.16 \(\int \genfrac {}{}{}{}{1}{36-13 x^2+x^4} \, dx\) [16]
  3.1.17 \(\int \genfrac {}{}{}{}{\log (\log (x))}{x} \, dx\) [17]
  3.1.18 \(\int \genfrac {}{}{}{}{1+\cot (x)}{1-\cot (x)} \, dx\) [18]
  3.1.19 \(\int \genfrac {}{}{}{}{\cos (x)+x \sin (x)}{x (x+\cos (x))} \, dx\) [19]
  3.1.20 \(\int \genfrac {}{}{}{}{1}{\sec (x)+\sin (x)} \, dx\) [20]
  3.1.21 \(\int \genfrac {}{}{}{}{1}{\sqrt {1+e^x+e^{2 x}}} \, dx\) [21]
  3.1.22 \(\int e^{x^2} x^3 \, dx\) [22]
  3.1.23 \(\int (-\genfrac {}{}{}{}{1}{\log ^2(x)}+\genfrac {}{}{}{}{1}{\log (x)}) \, dx\) [23]
  3.1.24 \(\int \sqrt {2-x} \sqrt {-1+x} \, dx\) [24]
  3.1.25 \(\int \genfrac {}{}{}{}{-1+x^6}{-1-x+x^3+x^4} \, dx\) [25]
  3.1.26 \(\int (2 \log (x)+\log ^2(x)) \, dx\) [26]
  3.1.27 \(\int \genfrac {}{}{}{}{2 x}{\sqrt {1-x^4}} \, dx\) [27]
  3.1.28 \(\int \genfrac {}{}{}{}{1+x^2}{1+x} \, dx\) [28]
  3.1.29 \(\int \genfrac {}{}{}{}{-2-2 \sin (x)+\sin ^2(x)+\sin ^3(x)}{1+2 \sin (x)+\sin ^2(x)} \, dx\) [29]
  3.1.30 \(\int \text {csch}^2(x) \, dx\) [30]
  3.1.31 \(\int \sec ^4(x) \tan ^2(x) \, dx\) [31]
  3.1.32 \(\int \sqrt {\csc (x)-\sin (x)} \, dx\) [32]
  3.1.33 \(\int \cos ^6(x) \, dx\) [33]
  3.1.34 \(\int \genfrac {}{}{}{}{1}{1+2 x^2+x^4} \, dx\) [34]
  3.1.35 \(\int \cos (\log (x)) \, dx\) [35]
  3.1.36 \(\int \sec (x) \, dx\) [36]
  3.1.37 \(\int \genfrac {}{}{}{}{1}{9 \cos ^2(x)+4 \sin ^2(x)} \, dx\) [37]
  3.1.38 \(\int \genfrac {}{}{}{}{1}{x^2 (1+x^4)^{3/4}} \, dx\) [38]
  3.1.39 \(\int \cos (x) \cos (3 x) \cos (5 x) \, dx\) [39]
  3.1.40 \(\int (\genfrac {}{}{}{}{1}{\log (x)}+\log (\log (x))) \, dx\) [40]
  3.1.41 \(\int \genfrac {}{}{}{}{1}{2+e^x} \, dx\) [41]
  3.1.42 \(\int \sqrt {\genfrac {}{}{}{}{x}{1-x^3}} \, dx\) [42]
  3.1.43 \(\int \genfrac {}{}{}{}{4 x}{1-x^4} \, dx\) [43]
  3.1.44 \(\int x^x (1+\log (x)) \, dx\) [44]
  3.1.45 \(\int \sqrt {6 x-x^2} \, dx\) [45]
  3.1.46 \(\int \sin ^{99}(x) \sin (101 x) \, dx\) [46]
  3.1.47 \(\int e^{e^{x^2}} x \, dx\) [47]
  3.1.48 \(\int \genfrac {}{}{}{}{-1+3 x-3 x^2+x^3}{1+4 x+6 x^2+4 x^3+x^4} \, dx\) [48]
  3.1.49 \(\int \sqrt {\genfrac {}{}{}{}{1-x}{1+x}} \, dx\) [49]
  3.1.50 \(\int \genfrac {}{}{}{}{1}{-1+\sqrt {x}} \, dx\) [50]
  3.1.51 \(\int \sqrt [4]{x} \log (x) \, dx\) [51]
  3.1.52 \(\int \genfrac {}{}{}{}{1}{(1+\sqrt {x}) \sqrt {x-x^2}} \, dx\) [52]
  3.1.53 \(\int \genfrac {}{}{}{}{1}{(1+\sqrt [4]{x})^{10} \sqrt {x}} \, dx\) [53]
  3.1.54 \(\int \sqrt {1-x^2} \, dx\) [54]
  3.1.55 \(\int \genfrac {}{}{}{}{1}{\sqrt {1-4 x-x^2}} \, dx\) [55]
  3.1.56 \(\int \log (\genfrac {}{}{}{}{1}{x}) \, dx\) [56]
  3.1.57 \(\int \genfrac {}{}{}{}{1}{1+\sin (x)} \, dx\) [57]
  3.1.58 \(\int \genfrac {}{}{}{}{\sqrt {x}}{\sqrt {2012-x}+\sqrt {x}} \, dx\) [58]
  3.1.59 \(\int \genfrac {}{}{}{}{-1+x}{(1+x) \sqrt {x+x^2+x^3}} \, dx\) [59]
  3.1.60 \(\int \genfrac {}{}{}{}{1+4 x+6 x^2+4 x^3+x^4}{-1+3 x-3 x^2+x^3} \, dx\) [60]
  3.1.61 \(\int (\cos (x) \log (x)+\genfrac {}{}{}{}{\sin (x)}{x}) \, dx\) [61]
  3.1.62 \(\int \genfrac {}{}{}{}{1}{-x+x^3} \, dx\) [62]
  3.1.63 \(\int \genfrac {}{}{}{}{x \arcsin (x)}{\sqrt {1-x^2}} \, dx\) [63]
  3.1.64 \(\int (1-x)^{99} x \, dx\) [64]
  3.1.65 \(\int \csc (x) \sin (4 x) \, dx\) [65]
  3.1.66 \(\int \genfrac {}{}{}{}{1}{(1+\sqrt [3]{x}) \sqrt {x}} \, dx\) [66]
  3.1.67 \(\int \genfrac {}{}{}{}{1}{\sqrt {-1+2 x^2}} \, dx\) [67]
  3.1.68 \(\int \genfrac {}{}{}{}{1}{\sqrt {-1+e^x}} \, dx\) [68]
  3.1.69 \(\int \genfrac {}{}{}{}{x}{4+x^4} \, dx\) [69]
  3.1.70 \(\int \genfrac {}{}{}{}{2}{(\cos (x)-\sin (x))^2} \, dx\) [70]
  3.1.71 \(\int x \coth (x) \text {csch}(x) \, dx\) [71]
  3.1.72 \(\int x^5 \sqrt {1+x^3} \, dx\) [72]
  3.1.73 \(\int \genfrac {}{}{}{}{-1+x^7}{\log (x)} \, dx\) [73]
  3.1.74 \(\int \sqrt {\csc (x)-\sin (x)} \, dx\) [74]
  3.1.75 \(\int (-2 \log (2 x)+\log (x^2)) \, dx\) [75]
  3.1.76 \(\int e^x \, dx\) [76]
  3.1.77 \(\int \genfrac {}{}{}{}{\cos (x) \log (x)-\genfrac {}{}{}{}{\sin (x)}{x}}{\log ^2(x)} \, dx\) [77]
  3.1.78 \(\int (-1+3 x-3 x^2+x^3) \, dx\) [78]
  3.1.79 \(\int \sqrt {12-3 x^2} \, dx\) [79]
  3.1.80 \(\int ((-3+x)^7+x-\sin (3-x)) \, dx\) [80]
  3.1.81 \(\int \sin (x) \sqrt {1+\tan ^2(x)} \, dx\) [81]
  3.1.82 \(\int \genfrac {}{}{}{}{-1+x^2-x^3+x^5}{-1+x-x^3+x^4} \, dx\) [82]
  3.1.83 \(\int \log (x) \, dx\) [83]
  3.1.84 \(\int \genfrac {}{}{}{}{1}{1-e^{-x}} \, dx\) [84]
  3.1.85 \(\int \cos ^2(x) \sin ^2(x) \, dx\) [85]
  3.1.86 \(\int \genfrac {}{}{}{}{\pi \sin (\pi \sqrt {x})}{\sqrt {x}} \, dx\) [86]
  3.1.87 \(\int \tan ^2(x) \, dx\) [87]
  3.1.88 \(\int e^{\sqrt [4]{x}} \, dx\) [88]
  3.1.89 \(\int \cos (x) \cot (x) \, dx\) [89]
  3.1.90 \(\int (2 \log (x)+\log ^2(x)) \, dx\) [90]
  3.1.91 \(\int \genfrac {}{}{}{}{x^3}{1+x^2} \, dx\) [91]
  3.1.92 \(\int \genfrac {}{}{}{}{1}{2-2 x+x^2} \, dx\) [92]
  3.1.93 \(\int \log (\sin (x)) \sin (x) \, dx\) [93]
  3.1.94 \(\int \genfrac {}{}{}{}{x}{1-x^4} \, dx\) [94]
  3.1.95 \(\int \sqrt {12-3 x^2} \, dx\) [95]
  3.1.96 \(\int \sec ^5(x) \tan ^3(x) \, dx\) [96]
  3.1.97 \(\int \genfrac {}{}{}{}{1}{1-\sin (x)} \, dx\) [97]
  3.1.98 \(\int \genfrac {}{}{}{}{1}{x \sqrt {-2+x^2}} \, dx\) [98]
  3.1.99 \(\int \log (x^2) \, dx\) [99]
  3.1.100 \(\int \sin (\sqrt [3]{x}) \, dx\) [100]