3.11 Integrals 1001 to 1059

  3.11.1 \(\int \sqrt {1+\coth ^2(x)} \text {sech}^2(x) \, dx\) [1001]
  3.11.2 \(\int \text {sech}^2(x) \sqrt {1+\tanh ^2(x)} \, dx\) [1002]
  3.11.3 \(\int \text {sech}^4(x) (-1+\text {sech}^2(x))^2 \tanh (x) \, dx\) [1003]
  3.11.4 \(\int e^{n \sinh (a+b x)} \sinh (2 a+2 b x) \, dx\) [1004]
  3.11.5 \(\int e^{n \sinh (a+b x)} \sinh (2 (a+b x)) \, dx\) [1005]
  3.11.6 \(\int e^{n \sinh (\genfrac {}{}{}{}{a}{2}+\genfrac {}{}{}{}{b x}{2})} \sinh (a+b x) \, dx\) [1006]
  3.11.7 \(\int e^{n \sinh (\genfrac {}{}{}{}{1}{2} (a+b x))} \sinh (a+b x) \, dx\) [1007]
  3.11.8 \(\int e^{n \cosh (a+b x)} \sinh (2 a+2 b x) \, dx\) [1008]
  3.11.9 \(\int e^{n \cosh (a+b x)} \sinh (2 (a+b x)) \, dx\) [1009]
  3.11.10 \(\int e^{n \cosh (\genfrac {}{}{}{}{a}{2}+\genfrac {}{}{}{}{b x}{2})} \sinh (a+b x) \, dx\) [1010]
  3.11.11 \(\int e^{n \cosh (\genfrac {}{}{}{}{1}{2} (a+b x))} \sinh (a+b x) \, dx\) [1011]
  3.11.12 \(\int \text {csch}(x) \log (\tanh (x)) \text {sech}(x) \, dx\) [1012]
  3.11.13 \(\int \text {csch}(2 x) \log (\tanh (x)) \, dx\) [1013]
  3.11.14 \(\int \cosh (a+b x) F(c,d,\sinh (a+b x),r,s) \, dx\) [1014]
  3.11.15 \(\int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx\) [1015]
  3.11.16 \(\int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx\) [1016]
  3.11.17 \(\int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx\) [1017]
  3.11.18 \(\int \text {sech}(x) (5-11 \text {sech}^2(x)) \tanh (x) \, dx\) [1018]
  3.11.19 \(\int \genfrac {}{}{}{}{\text {csch}^2(x)}{a+b \coth (x)} \, dx\) [1019]
  3.11.20 \(\int (a+b \coth (x))^n \text {csch}^2(x) \, dx\) [1020]
  3.11.21 \(\int \text {csch}^2(x) (-1+\sinh ^2(x)) \, dx\) [1021]
  3.11.22 \(\int (-1-\genfrac {}{}{}{}{1}{1-\coth ^2(x)}) \text {csch}^2(x) \, dx\) [1022]
  3.11.23 \(\int \genfrac {}{}{}{}{(a+b \coth (x)) \text {csch}^2(x)}{c+d \coth (x)} \, dx\) [1023]
  3.11.24 \(\int \genfrac {}{}{}{}{(a+b \coth (x))^2 \text {csch}^2(x)}{c+d \coth (x)} \, dx\) [1024]
  3.11.25 \(\int \genfrac {}{}{}{}{(a+b \coth (x))^3 \text {csch}^2(x)}{c+d \coth (x)} \, dx\) [1025]
  3.11.26 \(\int \cosh ^3(x) (a+b \cosh ^2(x))^3 \sinh (x) \, dx\) [1026]
  3.11.27 \(\int \cosh (x) \sinh ^3(x) (a+b \sinh ^2(x))^3 \, dx\) [1027]
  3.11.28 \(\int \cosh (x) \sinh (x) \sqrt {a+b \sinh ^2(x)} \, dx\) [1028]
  3.11.29 \(\int \text {csch}(x) \sqrt {1+\log ^2(\coth (x))} \text {sech}(x) \, dx\) [1029]
  3.11.30 \(\int \genfrac {}{}{}{}{\coth (\sqrt {x}) \text {csch}(\sqrt {x})}{\sqrt {x}} \, dx\) [1030]
  3.11.31 \(\int \genfrac {}{}{}{}{\cosh (\sqrt {x}) \sinh (\sqrt {x})}{\sqrt {x}} \, dx\) [1031]
  3.11.32 \(\int \genfrac {}{}{}{}{\text {sech}(\sqrt {x}) \tanh (\sqrt {x})}{\sqrt {x}} \, dx\) [1032]
  3.11.33 \(\int \genfrac {}{}{}{}{\sinh ^2(x)}{a+b \sinh (2 x)} \, dx\) [1033]
  3.11.34 \(\int \genfrac {}{}{}{}{\cosh ^2(x)}{a+b \sinh (2 x)} \, dx\) [1034]
  3.11.35 \(\int \genfrac {}{}{}{}{\sinh ^2(x)}{a+b \cosh (2 x)} \, dx\) [1035]
  3.11.36 \(\int \genfrac {}{}{}{}{\cosh ^2(x)}{a+b \cosh (2 x)} \, dx\) [1036]
  3.11.37 \(\int \genfrac {}{}{}{}{\tanh (c+d x)}{\sqrt {a \sinh ^2(c+d x)}} \, dx\) [1037]
  3.11.38 \(\int \genfrac {}{}{}{}{\coth (c+d x)}{\sqrt {a \cosh ^2(c+d x)}} \, dx\) [1038]
  3.11.39 \(\int x \cosh (2 x) \text {sech}(x) \, dx\) [1039]
  3.11.40 \(\int x \cosh (2 x) \text {sech}^2(x) \, dx\) [1040]
  3.11.41 \(\int x \cosh (2 x) \text {sech}^3(x) \, dx\) [1041]
  3.11.42 \(\int \sqrt {\text {csch}(x)} (x \cosh (x)-4 \text {sech}(x) \tanh (x)) \, dx\) [1042]
  3.11.43 \(\int \sinh (x) (\cosh (x)+\sinh (x)) \, dx\) [1043]
  3.11.44 \(\int \genfrac {}{}{}{}{1+\sinh ^2(x)}{1+\cosh (x)+\sinh (x)} \, dx\) [1044]
  3.11.45 \(\int x^5 \cosh ^7(a+b x^3) \sinh (a+b x^3) \, dx\) [1045]
  3.11.46 \(\int \genfrac {}{}{}{}{\cosh ^2(x)}{1+e^x} \, dx\) [1046]
  3.11.47 \(\int \text {sech}(x) \sqrt {1+\text {sech}(x)} \tanh ^3(x) \, dx\) [1047]
  3.11.48 \(\int \coth ^3(x) \text {csch}(x) \sqrt {1+\text {csch}(x)} \, dx\) [1048]
  3.11.49 \(\int \cosh ^x(x) (\log (\cosh (x))+x \tanh (x)) \, dx\) [1049]
  3.11.50 \(\int F^{a+b x} (\cosh (c+d x)+\sinh (c+d x))^n \, dx\) [1050]
  3.11.51 \(\int F^{a+b x} (\cosh (c+d x)-\sinh (c+d x))^n \, dx\) [1051]
  3.11.52 \(\int \genfrac {}{}{}{}{\cosh ^4(a+b x)-\sinh ^4(a+b x)}{\cosh ^4(a+b x)+\sinh ^4(a+b x)} \, dx\) [1052]
  3.11.53 \(\int \genfrac {}{}{}{}{\cosh ^3(a+b x)-\sinh ^3(a+b x)}{\cosh ^3(a+b x)+\sinh ^3(a+b x)} \, dx\) [1053]
  3.11.54 \(\int \genfrac {}{}{}{}{\cosh ^2(a+b x)-\sinh ^2(a+b x)}{\cosh ^2(a+b x)+\sinh ^2(a+b x)} \, dx\) [1054]
  3.11.55 \(\int \genfrac {}{}{}{}{\cosh (a+b x)-\sinh (a+b x)}{\cosh (a+b x)+\sinh (a+b x)} \, dx\) [1055]
  3.11.56 \(\int \genfrac {}{}{}{}{-\text {csch}(a+b x)+\text {sech}(a+b x)}{\text {csch}(a+b x)+\text {sech}(a+b x)} \, dx\) [1056]
  3.11.57 \(\int \genfrac {}{}{}{}{-\text {csch}^2(a+b x)+\text {sech}^2(a+b x)}{\text {csch}^2(a+b x)+\text {sech}^2(a+b x)} \, dx\) [1057]
  3.11.58 \(\int \genfrac {}{}{}{}{-\text {csch}^3(a+b x)+\text {sech}^3(a+b x)}{\text {csch}^3(a+b x)+\text {sech}^3(a+b x)} \, dx\) [1058]
  3.11.59 \(\int \genfrac {}{}{}{}{-\text {csch}^4(a+b x)+\text {sech}^4(a+b x)}{\text {csch}^4(a+b x)+\text {sech}^4(a+b x)} \, dx\) [1059]