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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]
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