# Quick integral

## Homework Statement

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

## 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?

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

Use double angle formula to convert the integrand.
$$\cos 2(bx) = 2\cos^2 (bx) -1$$
$$\int cos^{2}(bx)dx=\frac{1}{2} \int (cos 2(bx)+1)dx$$
Wow that makes it easier...haha always forget my trig identities. Cheers for the quick response.