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?

$$x^n\int e^x\ dx\ne\int x^ne^x\ dx$$
$$I_n=\int x^ne^x\ dx=x^n\int e^x\ dx-\int\left[\dfrac{d(x^n)}{dx}\int e^x\ dx\right]dx$$
$$\implies I_n=x^ne^x-nI_{n-1}$$
