Answer
$\dfrac {1}{75}\left( 5x^{3}-7\right) ^{5}+c$
Work Step by Step
$v=5x^{3}-7\Rightarrow dv=15x^{2}dx$
$$\int x^{2}\left( 5x^{3}-7\right) ^{4}dx=\int \dfrac {1}{15}\left( 5x^{3}-7\right) ^{4}\times 15x^{2}dx=\int \dfrac {1}{15}v^{4}dv=\dfrac {1}{15}\times \dfrac {1}{5}v^{5}+c=\dfrac {1}{75}\left( 5x^{3}-7\right) ^{5}+c$$
