What's the integral of $int cos^2(x) tan^3(x) dx$ ?

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Answer 1 · 2018-04-02T15:16:33

$-lnabs(cosx)+1/2cos^2x+C$

$cos^2(x) tan^3(x) = cos^2xsin^3x/cos^3x$

$= sin^2x/cosx sinx$

$= (1-cos^2x)/cosx sinx$

$int cos^2(x) tan^3(x) dx = int (1/cosx + cosx) sinx dx$

$= -lnabs(cosx)+1/2cos^2x+C$

What's the integral of int cos^2(x) tan^3(x) dxint cos^2(x) tan^3(x) dx?