What is #inttanh(2x)dx#?

1 Answer
sjc · Nam D.
Mar 8, 2018

#1/2ln(cosh2x)+C#

Explanation:

We will use the trick that:

#int(f'(x))/(f(x))dx=ln|f(x)|+C#

Given:#inttanh2x \ dx#

#=int(sinh2x)/(cosh2x)dx#

#1/2int(2sinh2x)/(cosh2x)dx#

#=1/2ln(cosh2x)+C# (since #f'(cosh2x)=2sinh2x#)

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