# Homework Help: Quick integral

1. May 10, 2012

### KingBigness

1. The problem statement, all variables and given/known data

$\int cos^{2}(bx)dx$

2. Relevant equations

3. The attempt at a solution

This integral popped up in my quantum mechanics class yesterday and I solved it through double substitution to get,
$\frac{x}{2} + sin(bx) * \frac{1}{4b}$.

My question is, someone in my class said there was an easier way to solve this that only took 2-3 lines. Does anyone here have any ideas on what that may be?

2. May 10, 2012

### sharks

Use double angle formula to convert the integrand.
$$\cos 2(bx) = 2\cos^2 (bx) -1$$
$$\int cos^{2}(bx)dx=\frac{1}{2} \int (cos 2(bx)+1)dx$$

3. May 10, 2012

### KingBigness

Re: Quick integral (Solved)

Wow that makes it easier...haha always forget my trig identities. Cheers for the quick response.