3.2.1 \(\int \genfrac {}{}{}{}{\arctan (c+d \coth (a+b x))}{x} \, dx\) [101]
3.2.2 \(\int x^2 \arctan (c+(i+c) \coth (a+b x)) \, dx\) [102]
3.2.3 \(\int x \arctan (c+(i+c) \coth (a+b x)) \, dx\) [103]
3.2.4 \(\int \arctan (c+(i+c) \coth (a+b x)) \, dx\) [104]
3.2.5 \(\int \genfrac {}{}{}{}{\arctan (c+(i+c) \coth (a+b x))}{x} \, dx\) [105]
3.2.6 \(\int x^2 \arctan (c-(i-c) \coth (a+b x)) \, dx\) [106]
3.2.7 \(\int x \arctan (c-(i-c) \coth (a+b x)) \, dx\) [107]
3.2.8 \(\int \arctan (c-(i-c) \coth (a+b x)) \, dx\) [108]
3.2.9 \(\int \genfrac {}{}{}{}{\arctan (c-(i-c) \coth (a+b x))}{x} \, dx\) [109]
3.2.10 \(\int \arctan (e^x) \, dx\) [110]
3.2.11 \(\int x \arctan (e^x) \, dx\) [111]
3.2.12 \(\int x^2 \arctan (e^x) \, dx\) [112]
3.2.13 \(\int \arctan (e^{a+b x}) \, dx\) [113]
3.2.14 \(\int x \arctan (e^{a+b x}) \, dx\) [114]
3.2.15 \(\int x^2 \arctan (e^{a+b x}) \, dx\) [115]
3.2.16 \(\int \arctan (a+b f^{c+d x}) \, dx\) [116]
3.2.17 \(\int x \arctan (a+b f^{c+d x}) \, dx\) [117]
3.2.18 \(\int x^2 \arctan (a+b f^{c+d x}) \, dx\) [118]
3.2.19 \(\int e^{-x} \arctan (e^x) \, dx\) [119]
3.2.20 \(\int \genfrac {}{}{}{}{\arctan (x)}{(-1+x)^3} \, dx\) [120]
3.2.21 \(\int \genfrac {}{}{}{}{\arctan (1+2 x)}{(4+3 x)^3} \, dx\) [121]
3.2.22 \(\int \arctan (\sqrt {1+x}) \, dx\) [122]
3.2.23 \(\int \genfrac {}{}{}{}{1}{(1+x^2) (2+\arctan (x))} \, dx\) [123]
3.2.24 \(\int \genfrac {}{}{}{}{1}{(a+a x^2) (b-2 b \arctan (x))} \, dx\) [124]
3.2.25 \(\int \genfrac {}{}{}{}{x+x^3+(1+x)^2 \arctan (x)}{(1+x)^2 (1+x^2)} \, dx\) [125]
3.2.26 \(\int -x^3 \arctan (\sqrt {x}-\sqrt {1+x}) \, dx\) [126]
3.2.27 \(\int -x^2 \arctan (\sqrt {x}-\sqrt {1+x}) \, dx\) [127]
3.2.28 \(\int -x \arctan (\sqrt {x}-\sqrt {1+x}) \, dx\) [128]
3.2.29 \(\int -\arctan (\sqrt {x}-\sqrt {1+x}) \, dx\) [129]
3.2.30 \(\int -\genfrac {}{}{}{}{\arctan (\sqrt {x}-\sqrt {1+x})}{x} \, dx\) [130]
3.2.31 \(\int -\genfrac {}{}{}{}{\arctan (\sqrt {x}-\sqrt {1+x})}{x^2} \, dx\) [131]
3.2.32 \(\int -\genfrac {}{}{}{}{\arctan (\sqrt {x}-\sqrt {1+x})}{x^3} \, dx\) [132]
3.2.33 \(\int -\genfrac {}{}{}{}{\arctan (\sqrt {x}-\sqrt {1+x})}{x^4} \, dx\) [133]
3.2.34 \(\int \genfrac {}{}{}{}{\arctan (\genfrac {}{}{}{}{c x}{\sqrt {a-c^2 x^2}})^m}{\sqrt {d-\genfrac {}{}{}{}{c^2 d x^2}{a}}} \, dx\) [134]
3.2.35 \(\int \genfrac {}{}{}{}{\arctan (\genfrac {}{}{}{}{c x}{\sqrt {a-c^2 x^2}})^2}{\sqrt {d-\genfrac {}{}{}{}{c^2 d x^2}{a}}} \, dx\) [135]
3.2.36 \(\int \genfrac {}{}{}{}{\arctan (\genfrac {}{}{}{}{c x}{\sqrt {a-c^2 x^2}})}{\sqrt {d-\genfrac {}{}{}{}{c^2 d x^2}{a}}} \, dx\) [136]
3.2.37 \(\int \genfrac {}{}{}{}{1}{\sqrt {d-\genfrac {}{}{}{}{c^2 d x^2}{a}} \arctan (\genfrac {}{}{}{}{c x}{\sqrt {a-c^2 x^2}})} \, dx\) [137]
3.2.38 \(\int \genfrac {}{}{}{}{1}{\sqrt {d-\genfrac {}{}{}{}{c^2 d x^2}{a}} \arctan (\genfrac {}{}{}{}{c x}{\sqrt {a-c^2 x^2}})^2} \, dx\) [138]
3.2.39 \(\int \genfrac {}{}{}{}{1}{\sqrt {d-\genfrac {}{}{}{}{c^2 d x^2}{a}} \arctan (\genfrac {}{}{}{}{c x}{\sqrt {a-c^2 x^2}})^3} \, dx\) [139]
3.2.40 \(\int \genfrac {}{}{}{}{\arctan (\genfrac {}{}{}{}{e x}{\sqrt {-\genfrac {}{}{}{}{a e^2}{b}-e^2 x^2}})^m}{\sqrt {a+b x^2}} \, dx\) [140]
3.2.41 \(\int \genfrac {}{}{}{}{\arctan (\genfrac {}{}{}{}{e x}{\sqrt {-\genfrac {}{}{}{}{a e^2}{b}-e^2 x^2}})^2}{\sqrt {a+b x^2}} \, dx\) [141]
3.2.42 \(\int \genfrac {}{}{}{}{\arctan (\genfrac {}{}{}{}{e x}{\sqrt {-\genfrac {}{}{}{}{a e^2}{b}-e^2 x^2}})}{\sqrt {a+b x^2}} \, dx\) [142]
3.2.43 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b x^2} \arctan (\genfrac {}{}{}{}{e x}{\sqrt {-\genfrac {}{}{}{}{a e^2}{b}-e^2 x^2}})} \, dx\) [143]
3.2.44 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b x^2} \arctan (\genfrac {}{}{}{}{e x}{\sqrt {-\genfrac {}{}{}{}{a e^2}{b}-e^2 x^2}})^2} \, dx\) [144]
3.2.45 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b x^2} \arctan (\genfrac {}{}{}{}{e x}{\sqrt {-\genfrac {}{}{}{}{a e^2}{b}-e^2 x^2}})^3} \, dx\) [145]
3.2.46 \(\int \genfrac {}{}{}{}{\arctan (c (a+b x)) \log (d (a+b x))}{a+b x} \, dx\) [146]
3.2.47 \(\int e^{c (a+b x)} \arctan (\sinh (a c+b c x)) \, dx\) [147]
3.2.48 \(\int e^{c (a+b x)} \arctan (\cosh (a c+b c x)) \, dx\) [148]
3.2.49 \(\int e^{c (a+b x)} \arctan (\tanh (a c+b c x)) \, dx\) [149]
3.2.50 \(\int e^{c (a+b x)} \arctan (\coth (a c+b c x)) \, dx\) [150]
3.2.51 \(\int e^{c (a+b x)} \arctan (\text {sech}(a c+b c x)) \, dx\) [151]
3.2.52 \(\int e^{c (a+b x)} \arctan (\text {csch}(a c+b c x)) \, dx\) [152]
3.2.53 \(\int \genfrac {}{}{}{}{(a+b \arctan (c x^n)) (d+e \log (f x^m))}{x} \, dx\) [153]