 Integrals involving trigonometric functions often rely on trigonometric identities. If you don't know your trigonometric identities, you should. But you can still evaluate trigonometric integrals. Remember, a problem exists whether or not you know how to solve it. So let's consider the integral of sine 3x cosine 2x. There's a formula for that, but who needs it? We can use integration by parts. So let's split this as u sine 3x and dv cosine 2x dx. Differentiating and integrating gives us. And so integration by parts gives us. So what can we do with this integral? We'll use integration by parts again. And to avoid going backwards, we'll make the choices for u and dv. Differentiating and integrating. And the second application of integration by parts gives us. Which we can simplify to. And dropping that back into our work in progress. Let's clean up the algebra a little bit, so we'll simplify to get. And notice that our integral sine 3x cosine 2x appears on both sides. And that means we can solve for it. So solving for this integral gives us. And so we have our antiderivative. Don't forget the plus c. As a general rule, you always have a choice. A lot of simple, small, easy steps. Or a few giant, difficult steps. You could memorize a lot of trigonometric identities. And try to remember when to use each one. Or you could use integration by parts and algebra. You can do either, but it's easier to master one thing.