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