Question

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

Answer 1

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`