Question

How do you integrate `int xe^xdx` using integration by parts?

Answer 1

Remember the formula for IBP: `int u(dv)/dxdx=uv-intv(du)/dxdx`

Let `u=x=>(du)/dx=1`
Let `(dv)/dx=e^x=>v=e^x`

Substitute into the IBP equation:
`int xe^xdx=xe^x-int e^x(1)dx`
`:. int xe^xdx=xe^x-int e^xdx`
`:. int xe^xdx=xe^x-e^x+c`