Answer
$\int x(-x^2-1)^3dx=-\frac{1}{8}(-x^2-1)^4+C$
Work Step by Step
Substitution:
$u=-x^2-1$
$\frac{du}{dx}=-2x$
$dx=-\frac{1}{2x}du$
$\int x(-x^2-1)^3dx=\int xu^3(-\frac{1}{2x}du)=\int-\frac{1}{2}u^3du=-\frac{1}{8}u^4+C=-\frac{1}{8}(-x^2-1)^4+C$
