Question

How do you integrate `f(x)=x^2sinx` using the product rule?

Answer 1

`int x^2 sin x dx= x^2 int sinx dx - int d/dx x^2 int sin x dx`

=`-x^2 cos x-int 2x (-cos x)dx`

=`-x^2 cos x +2int x cosx dx`

= -`x^2 cos x+2[x int cos x dx- int d/dx x int cos x dx`

=-`x^2 cosx+2[x sin x-int int cosxdx]`

=`-x^2cos x +2x sin x +2cos x +C`