Please could you help my solve this example:

Use integration by parts to solve:

 

Integral xsin(2x)dx

 

Many Thanks

Don't have time as I am at work and there are many better mathematicians than me here... but - define your terms u = .. and v = ... and sub them into the integration by parts equation.... which I can't remember off the top of my head (too many years ago).

 

u = x and v = sin2x ?? then put into the standard equation for the solution of integration by parts and do the sums.

 

I 'think' this is right... I am sure I someone else will let you know otherwise... Mr ajb, for example, is awesome at maths here.

This belongs in homework.

 

I will make a small adjustment to DrP's post

 

Integration by parts is for a product of two functions u(x) and v(x) but not directly multiplied, since one is a differential.

 

[math]\int udv = uv - \int vdu[/math]

 

 

You need to chose the u as the function that can most easily be differentiated and the dv as the function that can most easily be integrated.

(sometimes there is little to chose between)

 

So in this case chose u = x and dv = sin2x

 

Can you take it from here, you should have three terms in your answer

Thanks studiot... it's u and dv that you define not u and v as I said... thanks for correcting - I didn't have time to look it up.