Integral of a Radical

How to find the integral of a radical: formula, 1 example, and its solution.

Formula

Formula

When solving the integral of a radical,
first change the radical to a power with a rational exponent,
then use the formula below.

∫ xn dx = [1/(n + 1)]xn + 1 + C

Integral of a Polynomial

Example

Example

Solution

x = x1/2

The exponent of x1/2 is 1/2.
1/2 + 1 = 3/2
The reciprocal of 3/2 is 2/3.
So write 2/3.

1/2 + 1 = 3/2
So write x3/2.

The given integral is an indefinite integral.
So write +C.

x3/2 = x⋅x1/2

Product of Powers

x⋅x1/2 = x⋅√x.

So [2/3]x√x + C is the answer.