How do you find the antiderivative of $(1+cosx)^2$ ?

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Answer 1 · 2016-06-08T17:34:52

We have that

$int (1+cosx)^2 dx=int (1+2*cosx+cos^2x)dx=int 1dx+2*int cosx+int cos^2x dx$

First we notice that

$cos^2 x=1/2(1+cos2x)$

Hence

$int (1+cosx)^2 dx=int (1+2*cosx+cos^2x)dx=int 1dx+2*int cosx+int cos^2xdx=x+2*sinx+x/2+1/4*sin2x+c$

How do you find the antiderivative of (1+cosx)^2(1+cosx)^2?