3.3 Integrals 201 to 263

  3.3.1 \(\int \genfrac {}{}{}{}{1}{(a+b \tanh ^2(c+d x))^4} \, dx\) [201]
  3.3.2 \(\int \sqrt {1-\tanh ^2(x)} \, dx\) [202]
  3.3.3 \(\int \sqrt {-1+\tanh ^2(x)} \, dx\) [203]
  3.3.4 \(\int (1-\tanh ^2(x))^{3/2} \, dx\) [204]
  3.3.5 \(\int (-1+\tanh ^2(x))^{3/2} \, dx\) [205]
  3.3.6 \(\int \genfrac {}{}{}{}{1}{\sqrt {1-\tanh ^2(x)}} \, dx\) [206]
  3.3.7 \(\int \genfrac {}{}{}{}{1}{\sqrt {-1+\tanh ^2(x)}} \, dx\) [207]
  3.3.8 \(\int \tanh ^5(x) \sqrt {a+b \tanh ^2(x)} \, dx\) [208]
  3.3.9 \(\int \tanh ^4(x) \sqrt {a+b \tanh ^2(x)} \, dx\) [209]
  3.3.10 \(\int \tanh ^3(x) \sqrt {a+b \tanh ^2(x)} \, dx\) [210]
  3.3.11 \(\int \tanh ^2(x) \sqrt {a+b \tanh ^2(x)} \, dx\) [211]
  3.3.12 \(\int \tanh (x) \sqrt {a+b \tanh ^2(x)} \, dx\) [212]
  3.3.13 \(\int \sqrt {a+b \tanh ^2(x)} \, dx\) [213]
  3.3.14 \(\int \coth (x) \sqrt {a+b \tanh ^2(x)} \, dx\) [214]
  3.3.15 \(\int \coth ^2(x) \sqrt {a+b \tanh ^2(x)} \, dx\) [215]
  3.3.16 \(\int \coth ^3(x) \sqrt {a+b \tanh ^2(x)} \, dx\) [216]
  3.3.17 \(\int \coth ^4(x) \sqrt {a+b \tanh ^2(x)} \, dx\) [217]
  3.3.18 \(\int \coth ^5(x) \sqrt {a+b \tanh ^2(x)} \, dx\) [218]
  3.3.19 \(\int \tanh ^3(x) (a+b \tanh ^2(x))^{3/2} \, dx\) [219]
  3.3.20 \(\int \tanh ^2(x) (a+b \tanh ^2(x))^{3/2} \, dx\) [220]
  3.3.21 \(\int \tanh (x) (a+b \tanh ^2(x))^{3/2} \, dx\) [221]
  3.3.22 \(\int (a+b \tanh ^2(x))^{3/2} \, dx\) [222]
  3.3.23 \(\int \coth (x) (a+b \tanh ^2(x))^{3/2} \, dx\) [223]
  3.3.24 \(\int \coth ^2(x) (a+b \tanh ^2(x))^{3/2} \, dx\) [224]
  3.3.25 \(\int \sqrt {1+\tanh ^2(x)} \, dx\) [225]
  3.3.26 \(\int \sqrt {-1-\tanh ^2(x)} \, dx\) [226]
  3.3.27 \(\int (1+\tanh ^2(x))^{3/2} \, dx\) [227]
  3.3.28 \(\int (-1-\tanh ^2(x))^{3/2} \, dx\) [228]
  3.3.29 \(\int \genfrac {}{}{}{}{\tanh ^5(x)}{\sqrt {a+b \tanh ^2(x)}} \, dx\) [229]
  3.3.30 \(\int \genfrac {}{}{}{}{\tanh ^4(x)}{\sqrt {a+b \tanh ^2(x)}} \, dx\) [230]
  3.3.31 \(\int \genfrac {}{}{}{}{\tanh ^3(x)}{\sqrt {a+b \tanh ^2(x)}} \, dx\) [231]
  3.3.32 \(\int \genfrac {}{}{}{}{\tanh ^2(x)}{\sqrt {a+b \tanh ^2(x)}} \, dx\) [232]
  3.3.33 \(\int \genfrac {}{}{}{}{\tanh (x)}{\sqrt {a+b \tanh ^2(x)}} \, dx\) [233]
  3.3.34 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \tanh ^2(x)}} \, dx\) [234]
  3.3.35 \(\int \genfrac {}{}{}{}{\coth (x)}{\sqrt {a+b \tanh ^2(x)}} \, dx\) [235]
  3.3.36 \(\int \genfrac {}{}{}{}{\coth ^2(x)}{\sqrt {a+b \tanh ^2(x)}} \, dx\) [236]
  3.3.37 \(\int \genfrac {}{}{}{}{\coth ^3(x)}{\sqrt {a+b \tanh ^2(x)}} \, dx\) [237]
  3.3.38 \(\int \genfrac {}{}{}{}{\tanh ^5(x)}{(a+b \tanh ^2(x))^{3/2}} \, dx\) [238]
  3.3.39 \(\int \genfrac {}{}{}{}{\tanh ^4(x)}{(a+b \tanh ^2(x))^{3/2}} \, dx\) [239]
  3.3.40 \(\int \genfrac {}{}{}{}{\tanh ^3(x)}{(a+b \tanh ^2(x))^{3/2}} \, dx\) [240]
  3.3.41 \(\int \genfrac {}{}{}{}{\tanh ^2(x)}{(a+b \tanh ^2(x))^{3/2}} \, dx\) [241]
  3.3.42 \(\int \genfrac {}{}{}{}{\tanh (x)}{(a+b \tanh ^2(x))^{3/2}} \, dx\) [242]
  3.3.43 \(\int \genfrac {}{}{}{}{1}{(a+b \tanh ^2(x))^{3/2}} \, dx\) [243]
  3.3.44 \(\int \genfrac {}{}{}{}{\coth (x)}{(a+b \tanh ^2(x))^{3/2}} \, dx\) [244]
  3.3.45 \(\int \genfrac {}{}{}{}{\coth ^2(x)}{(a+b \tanh ^2(x))^{3/2}} \, dx\) [245]
  3.3.46 \(\int \genfrac {}{}{}{}{\tanh ^6(x)}{(a+b \tanh ^2(x))^{5/2}} \, dx\) [246]
  3.3.47 \(\int \genfrac {}{}{}{}{\tanh ^5(x)}{(a+b \tanh ^2(x))^{5/2}} \, dx\) [247]
  3.3.48 \(\int \genfrac {}{}{}{}{\tanh ^4(x)}{(a+b \tanh ^2(x))^{5/2}} \, dx\) [248]
  3.3.49 \(\int \genfrac {}{}{}{}{\tanh ^3(x)}{(a+b \tanh ^2(x))^{5/2}} \, dx\) [249]
  3.3.50 \(\int \genfrac {}{}{}{}{\tanh ^2(x)}{(a+b \tanh ^2(x))^{5/2}} \, dx\) [250]
  3.3.51 \(\int \genfrac {}{}{}{}{\tanh (x)}{(a+b \tanh ^2(x))^{5/2}} \, dx\) [251]
  3.3.52 \(\int \genfrac {}{}{}{}{1}{(a+b \tanh ^2(x))^{5/2}} \, dx\) [252]
  3.3.53 \(\int \genfrac {}{}{}{}{\coth (x)}{(a+b \tanh ^2(x))^{5/2}} \, dx\) [253]
  3.3.54 \(\int \genfrac {}{}{}{}{\coth ^2(x)}{(a+b \tanh ^2(x))^{5/2}} \, dx\) [254]
  3.3.55 \(\int \genfrac {}{}{}{}{1}{\sqrt {1+\tanh ^2(x)}} \, dx\) [255]
  3.3.56 \(\int \genfrac {}{}{}{}{1}{\sqrt {-1-\tanh ^2(x)}} \, dx\) [256]
  3.3.57 \(\int (a+b \tanh ^3(c+d x))^2 \, dx\) [257]
  3.3.58 \(\int \genfrac {}{}{}{}{1}{1+\tanh ^3(x)} \, dx\) [258]
  3.3.59 \(\int \tanh (x) (a+b \tanh ^4(x))^{3/2} \, dx\) [259]
  3.3.60 \(\int \tanh (x) \sqrt {a+b \tanh ^4(x)} \, dx\) [260]
  3.3.61 \(\int \genfrac {}{}{}{}{\tanh (x)}{\sqrt {a+b \tanh ^4(x)}} \, dx\) [261]
  3.3.62 \(\int \genfrac {}{}{}{}{\tanh (x)}{(a+b \tanh ^4(x))^{3/2}} \, dx\) [262]
  3.3.63 \(\int \genfrac {}{}{}{}{\tanh (x)}{(a+b \tanh ^4(x))^{5/2}} \, dx\) [263]