I need help! I need to solve the integral of cos(ax)sin(bx), but I can't get it to what the answer is. Help! :(

Question

jamesj · Answer

Let $$ I = \int \cos(ax) \sin(bx) \ dx $$
and integrate twice by parts until you get the integral I back.  In other words, you will obtain an expression  that looks like this
$$ I = (expression \ involving \ cos \ and \ sin ) + (some \ constant) I $$

Then solve algebraically for $I$.

anonymous · Answer

At the end though, wouldn't it be I = (expression) - (some constant)I? I don't want to get confused...haha

That's the only difference I have in my work for it

jamesj · Answer

C'mon.  That's a trivial difference, as the question is whether or not the constant has 
the -1 or not.  +C = -(-C)

anonymous · Answer

Okay, okay. Just asking.

jamesj · Answer

So integrating once
$$ I = 1/a . \sin ax . \sin bx - b/a \int \sin ax . \cos bx \ dx $$
Now integrate again.

anonymous · Answer

Okay, I have that done. It just gets messy after that