Find the value of ∫xexdx
Finding the value of ∫xexdx
Let, I=∫xexdx
We know that,
∫uvdx=u∫vdx-∫(ddx(u)∫vdx)dx
So,
I=x∫exdx-∫d(x)dx(∫exdx)dx=xex-∫1.exdx=xex-ex+c
Hence the value of ∫xexdx is xex-ex+c