Question

1. x sin x

Answer 1

The integral is given as follows,

I= ∫ xsinxdx

Use integration by parts rule. Consider x as first function and sinxas second function.

I=x ∫ sinxdx− ∫ ( d dx x ∫ sinxdx )dx =x( −cosx )− ∫ ( −cosx )dx =−xcosx+sinx+C

Thus, the integration of ∫ xsinxdx is −xcosx+sinx+C.