CUET PG 2024 — Mathematics PYQ

$\int \frac{(x^2-x{)}^{1/5}}{x^6}dx$

$=\int \frac{x^6(1-\frac{1}{x^4}{)}^{1/5}}{x^6}dx$

$\text{Put }1-\frac{1}{x^4}=t$

$\frac{4}{x^5}dx=dt$

$\frac{1}{4}\int t^{1/5}dt$

$=\frac{5}{24}{t}^{6/5}+C$

$=\frac{5}{24}{\left(1-\frac{1}{x^4}\right)}^{6/5}+C$