How do you evaluate the integral $int sec^2x/(1+tanx)dx$ ?

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Answer 1 · 2017-01-02T15:56:30

$intsec^2x/(1 + tanx)dx = ln|1 + tanx| + C$

This is a u-subsitution problem. Our goal is to cancel out the numerator. Let $u = 1 + tanx$ . Then $du = sec^2xdx$ and $dx= (du)/sec^2x$

$=intsec^2x/u * (du)/sec^2x$

$= int(1/u) du$

This can be integrated as $int(1/x)dx = ln|x| + C$ .

$= ln|u| + C$

$= ln|1 + tanx| + C$ , where $C$ is a constant

Hopefully this helps!

How do you evaluate the integral int sec^2x/(1+tanx)dxint sec^2x/(1+tanx)dx?