Answer
$\int\frac{x^2+x^5}{\sqrt {2x^3+x^6-5}}dx=\frac{1}{3}\sqrt {2x^3+x^6-5}+C$
Work Step by Step
Substitution:
$u=2x^3+x^6-5$
$\frac{du}{dx}=6x^2+6x^5=6(x^2+x^5)$
$dx=\frac{1}{6(x^2+x^5)}du$
$\int\frac{x^2+x^5}{\sqrt {2x^3+x^6-5}}dx=\int\frac{x^2+x^5}{u^{\frac{1}{2}}}\frac{1}{6(x^2+x^5)}du=\int\frac{1}{6}u^{-\frac{1}{2}}du=\frac{1}{6}\frac{u^{\frac{1}{2}}}{\frac{1}{2}}+C=\frac{1}{3}\sqrt {2x^3+x^6-5}+C$
