Answer
$-\displaystyle \frac{1}{40}(5x^{4}-4x^{5})^{-4}+C$
Work Step by Step
$I=\displaystyle \int\frac{2(x^{3}-x^{4})}{(5x^{4}-4x^{5})^{5}}dx=\quad$
Substitute:
$ \left[\begin{array}{llll}
u & =5x^{4}-4x^{5} & & \\
du & =(20x^{3}-20x^{4})dx & & \\
& =20(x^{3}-x^{4}) & \Rightarrow & 2(x^{3}-x^{4})dx=\frac{du}{10}
\end{array}\right]$
$I=\displaystyle \int\frac{1}{u^{5}}\cdot\frac{du}{10}=\frac{1}{10}\int u^{-5}du$
$=\displaystyle \frac{1}{10}\cdot\frac{u^{-4}}{-4}+C$
bring back the variable $x$
= $-\displaystyle \frac{1}{40}(5x^{4}-4x^{5})^{-4}+C$
