Do you have to do it by parts? If not you can do it by log differentiation and it's much simpler:
Let y=−xexsinx
Log both sides. We know ln(abc) = lna + lnb + lnc. Use this to split the expression and then differentiate wrt x (remembering left hand side is implicit, so you get 1/y dy/dx)
Once you multiply up by the y and put in a nicer form you will get the required answer
It's a tricky one. You need to use IBP 3 times and also be able to spot the trick for integrating things of the form ekxsin(nx). The answer isn't that messy.