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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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2.46 Algebraic functions of hyperbolic functions

2.461

1. 

tanh x dx = archtanh tanh x  archtan tanh x

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MZ 221

2. 

coth x dx=arccothcoth x arctan coth x  

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2.462

1. 

sinh x dxa2+sinh2x=arcsinhcosh xa21=ln (cosh x+a2+sinh2x)[ a2>1]=arccoshcosh x1a2=ln (cosh x+a2+sinh2x)[ a2<1]=ln cosh x[ a2=1]

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2. 

sinh x dxa2sinh2x=arcsincosh xa2+1                [ sinh2x<a2]

3. 

sinh x dxsinh2xa2=arccoshcosh xa2+1=ln(cosh x+sinh2xa2)          

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