Finding intergral?

Question

Int((x^2)sin(x) dx)

Any ideas where to start?


Thanks!

Answer 1

By partial integration: int(x^2sin(x)dx) = - x^2 cos(x) + int(2xcos(x)dx) = - x^2cos(x) + 2xsin(x) - 2int(sin(x)dx) = - x^2cos(x) + 2xsin(x) + 2cos(x).

Answer 2

Use partial integration (at *):

(Check the signs, cause they are wrong and I don't care ;) )

Int(x² sinx dx) = Int(x² d cosx) =* x²cosx - Int(cosx dx²) = x²cosx - 2 Int(x cosx dx)

Int(x cosx dx) = Int(x d sinx) =* xsinx - Int(sin x dx)

...

So general rule is Int(f dg) = f.g - Int(g df).

Answer 3

put x^2=u and sinxdx as dv and integrate by parts