Answer
$-\frac{1}{3}$$\ln|5-x^{3}|$ + C
Work Step by Step
$\int\frac{x^{2}}{5-x^{3}} dx $
Let $u =5-x^{3}$
$\frac{du}{dx}$ = $-3x^{2}$
$\frac{du}{-3x^{2}}$ = $dx$
Substitute $u$ and $dx$ into the original equation
$\int\frac{x^{2}}{u}\frac{du}{-3x^{2}}$
= $\int\frac{x^{2}}{-3x^{2}}\frac{1}{u} du$
= $\int\frac{1}{-3}\frac{1}{u} du$
= $-\frac{1}{3}$$\int\frac{1}{u} du$
= $-\frac{1}{3}$$\ln|u|$ + C
Since $u =5-x^{3}$, substituting it back will give you
$-\frac{1}{3}$$\ln|5-x^{3}|$ + C
