用分部积分法求 积分x^2*e^xdx

Answer 1

by part twice,两次部分积分

=∫x²e^x+2xe^x-2xe^x dx
=x²e^x-2∫xe^x dx
=x²e^x-2∫xe^x +e^x-e^x dx
=x²e^x-2(xe^x -∫e^x dx)
=(x²-2x+2)e^x +C

Answer 2

原式=∫x²d(e^x)
=x²e^x-∫e^xd(x²)
=x²e^x-2∫xe^xdx
=x²e^x-2(x-1)e^x+c