# Math Help - Solve The Following Trigonometric Integral. (3)

1. ## Solve The Following Trigonometric Integral. (3)

Hello
here is it:
$\int ( cos(x) + 1 )^{\frac{3}{2}} dx$
I used $u=cos(x)+1$
Then, I got :
$- \int \frac{u^{\frac{3}{2}} }{ \sqrt{ 1 - (u-1)^2 }} du$
Using the trigonometric substitution $u-1=sin(\theta)$, I got:
$- \int (sin(\theta) + 1)^{\frac{3}{2}} du$

I think I will do the same work again and I will get the original integral in another variable.
then I will moved it the left hand side.
Since $\int f(x) dx = \int f(u) du = \int f(\theta) d\theta ....$
And I will devide by the resulting coefficient.
I think you understood what I mean.

2. Hint: $\cos x=2\cos ^{2}\frac{x}{2}-1.$