Question

Integrate the function: $\frac {x^2}{\sqrt {x^6+a^6}}$

Answer 1

$Let \ x^3 = t$

$⇒ 3x^2 dx = dt$

$∴ ∫\frac {x^2}{\sqrt {x^6+a^6}} dx = \frac 13 ∫\frac {dt}{\sqrt {t^2+(a^3)^2}}$

$=\frac 13\ log\ |t+\sqrt {t^2+a^6}|+C$

$=\frac 13\ log\ |x^3+\sqrt {x^6+a^6}|+C$