Integration by Parts Question: Integrate $x^3e^x$ Evaluate $$\int x^3e^x \mathrm{d}x$$
I tried to use integration by parts to do this and I let $u = x^3$ and $\mathrm{d}v = e^x \mathrm{d}x$. So I get $$\int x^3e^x \mathrm{d}x= \int x^3e^x \mathrm{d}x- \int e^x \cdot 3x^2\mathrm{d}x$$
How do I do this if my answer has the original integral in it?

Hint: Notice that you are applying it (Integration by parts Formula) wrong. It should go as
$$\int x^3 e^x dx = x^3 e^x - 3\int x^2 e^x dx$$
Apply it twice and see what you find. 
