How to Integrate the Cube Root of X

By Lynn Wood; Updated April 24, 2017
A simple rule allows you to integrate equations involving fractional powers.

In calculus, the easiest way to deal with roots is to turn them into fraction powers. A square root will become a ½ power, a cube root will become a 1/3 power and so on. There is a basic formula to follow when taking the integral of an expression with a power 1/(n+1) x^(n+1).

Re-write the cube root into a fraction power: x^(1/3).

Add one to the power: x^(4/3).

Multiply the expression by the reciprocal of the power. A reciprocal is simply a fraction flipped. For example the reciprocal of 4/3 is 3/4. Multiplying by 3/4 yields: 3/4 x^(4/3).

About the Author

Lynn Wood is a professional writer who grew up on a dairy farm in rural Missouri. After completing her bachelor's degree in English and journalism at Brigham Young University-Idaho, she stayed there and taught in the university's math department for three years before settling down in Preston, Idaho. Wood now teaches high-school English.