# Integral of a Radical

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

## Formula

When solving the integral of a radical,

first change the radical to a power with a rational exponent,

then use the formula below.

∫ x^{n} dx = [1/(n + 1)]x^{n + 1} + C

Integral of a Polynomial

## Example∫ √x dx

Solution

Solution (Detail)

√x = x^{1/2}

The exponent of x^{1/2} 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 x^{3/2}.

The given integral is an indefinite integral.

So write +C.

x^{3/2} = x⋅x^{1/2}

Product of Powers

x⋅x^{1/2} = x⋅√x.

So

[2/3]x√x + C

is the answer.