Question

Evaluate: $\int \frac{x^2}{1+x^6}dx$

Answer 1

$\int \frac{x^2}{1+x^6}=\frac{d{x}^2}{1+(x^3{)}^2}\Rightarrow x^3=t$ $3x^{2}dx=dt$

$\Rightarrow \int \frac{1}{3}\left(\frac{1}{1+t^2}\right)\Rightarrow \frac{1}{3}ta{n}^{-1}t+c\Rightarrow \frac{1}{3}ta{n}^{-1}\left(x^3\right)+c$