Math Help - Integral of Trig function

1. Integral of Trig function

2∫cos²x dx

I have trouble solving I tried using u substitution many times and trying to use the identities but I can not some how figure it out. Can someone show me?

2. Originally Posted by superman69
2∫cos²x dx

I have trouble solving I tried using u substitution many times and trying to use the identities but I can not some how figure it out. Can someone show me?
You don't want u-substitution. We have the trig identity: $\cos(2x)=2\cos^2(x)-1$. Therefore,

$\int2\cos^2(x)\,dx=\int(\cos(2x)+1)\,dx=\frac{1}{2 }\sin(2x)+x+C$

3. I didn't get where the 2 went from 2∫cos²x

4. Originally Posted by superman69
I didn't get where the 2 went from 2∫cos²x
$2\int\cos^2x\,dx=\int2\cos^2x\,dx$

It's one of the rules of integrals.