1. ## Trigonometric integral

$\int sin(x)cos(nx)dx$ where n is a positive entire
Thank's.

2. $\displaystyle sin(A)cos(B)=\frac{sin(A-B) + sin(A+B)}{2}$

3. Use $2\sin mx\cos nx=\sin (m+n)x+\sin (m-n)x$ .

Edited: Sorry, I didn't see General's post.

4. You could also integrate by parts twice and solve for the original integral.