Answer
$\int3x\sqrt {-x^2+1}dx=-(-x^2+1)^{\frac{3}{2}}+C$
Work Step by Step
Substitution:
$u=-x^2+1$
$\frac{du}{dx}=-2x$
$dx=-\frac{1}{2x}du$
$\int3x\sqrt {-x^2+1}dx=\int3x\sqrt {u}(-\frac{1}{2x})du=\int-\frac{3}{2}u^{\frac{1}{2}}du=-\frac{3}{2}\frac{u^\frac{3}{2}}{\frac{3}{2}}+C=-u^\frac{3}{2}+C=-(-x^2+1)^{\frac{3}{2}}+C$
