Answer
The required formula is $$\int z^3 dz=\frac{z^4}{4}+c.$$
Work Step by Step
The integral $$\int x(x^2+1)^3dx$$ with the substitution $z=x^2+1$ where $dz=2xdx$ can be transformed into integral $$\frac{1}{2}\int z^3dz,$$ so we need to use formula $$\int z^3 dz=\frac{z^4}{4}+c.$$
