What's the integral of $int sin(x)tan(x) dx$ ?

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Answer 1 · 2015-11-21T17:19:02

$intsin(x)tan(x)dx = ln|sec(x) + tan(x)| - sin(x) + c$

We have

$intsin(x)tan(x)dx$

Or, in other terms

$intsin^2(x)/cos(x)dx$

Or, since $sin^2(x) = 1 - cos^2(x)$

$int(1 - cos^2(x))/cos(x)dx$

Doing the fraction we have

$int(sec(x) - cos(x))dx$

Break the integral into fractions

$intsec(x)dx - intcos(x)dx$

And those are standard integrals, so evaluate that

$intsin(x)tan(x)dx = ln|sec(x) + tan(x)| - sin(x) + c$

What's the integral of int sin(x)tan(x) dxint sin(x)tan(x) dx?