Answer
$=\frac{5}{4}f^4(x)+\frac{7}{3}f^3(x)+\frac{1}{2}f^2(x)+c$
Work Step by Step
$\int(5f^3(x)+7f^2(x)+f(x))f'(x)dx$
$u=f(x)$
$dx=\frac{du}{f'(x)}$
$\int(5u^3+7u^2+u)du=\int5u^3du+\int7u^2du+\int u*du$
$=\frac{5}{4}u^4+\frac{7}{3}u^3+\frac{1}{2}u^2+c$
$=\frac{5}{4}f^4(x)+\frac{7}{3}f^3(x)+\frac{1}{2}f^2(x)+c$
