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