integrate this: (x^3)/(7+x^8) dx

Question

please use u-substitution

Answer 1

From the Table of Integrals:  ∫(du/(u² + a²)) = (1/a)tan^-1(u/a)

 

Let u = x⁴, then u² = x⁸, and let a = √(7), a² = 7.

 

du = 4x³dx or (1/4)du = x³dx

 

∫(x³dx/(x⁸ + 7)) = (1/4)(1/√(7))tan^-1(x⁴/√(7)) + C

 

A²