Evaluate $\int x^3(x^2+7)\ dx$ I'm trying to find the indefinite integral of $$\int x^3(x^2+7)\ dx$$ and I've seem to have forgotten how to do it in this case. So if anyone can refresh my memory, I'd appreciate it.

First expand the integrand.
It simplifies to $x^5+7x^3$. Then we have that
$$\int x^5 + 7x^3=\frac{x^6}{6}+\frac{7x^4}{4}+C$$
This is done by the Power Rule, i.e, $$\int x^n\ dx=\frac{x^{n+1}}{n+1}+C$$
