Question

$\int\limits^1_0 {\frac{x^{2}}{1+x^6}} \, dx$

Answer 1

int x²/(1+x⁶) dx = int x²/(1+(x³)²) dx =
= 1/3 int (x³)'/(1+(x³)²) dx =
= 1/3•arctg(x³) dx

=> int₀¹ x²/(1+x⁶) dx =
= 1/3•arctg(1) - 1/3•arctg(0) = pi/12