How to Integrate the Cube Root of X

A simple rule allows you to integrate equations involving fractional powers.
••• Cristina Dumitras/iStock/Getty Images

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).

Related Articles

How to Take the Natural Log of a Fraction With X in...
How to Classify Polynomials by Degree
How to Simplify Exponents
How to Find Resistance With Power & Voltage
How to Solve Large Exponents
How to Calculate the Slope of a Curve
How to Calculate a KVA Rating
How to Manipulate Roots & Exponents
How to Linearize a Power Function
How to Take the Natural Log of a Fraction With X in...
How to Divide Rational Numbers
What Happens When You Raise a Number to a Fraction?
How to Convert Slope Intercept Form to Standard Form
How to Do Fractions With a TI 83 Calculator
How to Find the X Intercept of a Function
How to Use a Variac
How to Integrate Sin^2 X
How to Put a Cube Root Into a Graphing Calculator