Question

Integrate the function: $\frac {3x^2}{x^6+1}$

Answer 1

$Let\ x^3 = t$

$∴ 3x^2 dx = dt$

$⇒ ∫\frac {3x^2}{x^6+1}dx = ∫\frac {dt}{t^2+1}$

$=tan^{-1} t+C$

$=tan^{-1} (x^3)+C$