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

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Answer 1 · 2017-02-19T18:17:10

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

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

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

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

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

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

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