Answer
$\frac{(5+x^4)^\frac{3}{2}}{6}+C$
Work Step by Step
Use the substitution $u=5+x^4$. Then $du=4x^3dx$, so $x^3dx=\frac{1}{4}du$.
$\int x^3\sqrt{5+x^4} dx$
$=\int \sqrt{u}*\frac{1}{4}du$
$=\frac{u^\frac{3}{2}}{\frac{3}{2}}*\frac{1}{4}+C$
$=\frac{u^\frac{3}{2}}{6}+C$
$=\frac{(5+x^4)^\frac{3}{2}}{6}+C$
