What is the solution to $int e^x/(1 - e^(2x))^(1/2) dx$ ?

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Answer 1 · 2017-03-03T17:59:08

$int e^x/(1 - e^(2x))^(1/2)dx = arcsin(e^x) + C$

We can write this as

$int e^x/sqrt(1 - (e^x)^2)$

It becomes clear that a u-subsittution of $u = e^x$ would be beneficial. This means that $du = e^xdx$ and $dx= (du)/e^x$ .

$int e^x/sqrt(1 - u^2) * (du)/e^x$

$int 1/sqrt(1 - u^2) du$

This is a known integral.

$arcsinu +C$

$arcsin(e^x) +C$

Hopefully this helps!

What is the solution to int e^x/(1 - e^(2x))^(1/2) dxint e^x/(1 - e^(2x))^(1/2) dx?