what is the antiderivative of: the cubed root of x +5/x^6

Question

this is a calculus prblem on anti derivatives and integrals. please help.

Answer 1

The only way this can be elementary integral is if the function is

 

f(x) = x^1/3 + 5/x⁶

 

since for all other combinations, Wolfram|Alpha gives an answer in terms of the Hypergeometric function ₂F₁(a,b;c;x).

 

∫ (x^1/3 + 5/x⁶)∫ (x^1/3 + 5x^-6) dx = 3x^4/3/4 - x^-5 + C = 3x^4/3 - 1/x⁵ + C