Question

Find $\int \frac{(x^4-x{)}^{1/4}}{x^5}dx$

Answer 1

$\int \frac{x(1-\frac{1}{x^3})}{x^5}dx$

$\frac{1}{3}\int 3\frac{(1-\frac{1}{x^3})}{x^4}dx$ $1-\frac{1}{x^3}=t$

$\frac{1}{3}\int tdt$ $\frac{3}{x^4}=dt$

$\frac{t^2}{6}+c$

$\frac{(1-\frac{1}{x^3}{)}^2}{6}+c$