How do you integrate (u+v)sin(u-v) with respect to u? Please help.

Question

anonymous · Answer

I know I should separate this into 2 equations ... usin(u-v) + vsin(u-v) but  not sure what to do from here

inkyvoyd · Answer

hint: sin(x+y)=sin x cos y+sin y cos x

inkyvoyd · Answer

bigger hint: sin(x-y)=sin x cos y-sin y cos x

anonymous · Answer

so would the answer be 1/2 (u+v)^2 x sin(u-v) + sinucosv - sinvcosu ???

inkyvoyd · Answer

NOt sure, let me check with mathematica.

anonymous · Answer

Yes, just follow the formula!

anonymous · Answer

Then split them out!

inkyvoyd · Answer

http://www.wolframalpha.com/input/?i=Integrate%5B%28u+%2B+v%29+Sin%5Bu+-+v%5D%2C+x%5D

inkyvoyd · Answer

Input;Integrate[(u + v) Sin[u - v], x]
Output:(u + v) x Sin[u - v]

anonymous · Answer

okay so did I do it right? I followed the formula but i'm not sure if thats right. I'm not too sure. I know how to integrate I just forget how to integrate when there's ( ) or trig functions being multiplied to something else

inkyvoyd · Answer

it could be that you didn't rewrite it into that form

anonymous · Answer

The formula provide from @inkyvoyd is correct! Follow it, you're on the right track :)
Because it is sum -> split them out!

anonymous · Answer

okay thank you guys =)