Answer to Question #204957 in Calculus for Carlos

Question

Solve the integral of x²cosxdx, using integration by parts.

Answer 1

$\int x^2cos(x)dx=x^2sin(x)- \int sin(x).2xdx=x^2.sin(x)-2\int x.sin(x)dx$

$u=x^2 \space \space \space du=2x \space dx$

$dv=cos(x)dx \space \space \space v=sin(x)$

$x^2sin(x)-2(x.(-cos(x)- \int-cos(x)dx)=x^2sin(x)-2(-xcos(x)+ \int cos(x)dx$

$u=x \space \space \space \space du=dx$

$dv=sin(x)dx \space \space \space \space \space v=-cos(x)$

$=x^2.sin(x)+2xcos(x)-2sin(x)+C$