How to integrate sqrt (1+x^3) ?

First integrate the entire thing by letting multiplying by 1/2 the entire expression raised to exponent 1/2 - 1. That is,

0.5 (1 + x³) ^-0.5

Then, multiplying this by the derivative of those inside the parentheses. The final answer would be,

(0.5) ((1 + x³) ^-0.5) (3x²)