# Finding the indefinite integral

## Homework Statement

$\int$(x^(1/3)/(x^(1/3)+1))dx

## Homework Equations

I know I have to use u substitution
u=x^(1/3)
du=1/(3x^(2/3))dx

## The Attempt at a Solution

I know that the denominator of the equation will be u+1, but I don't understand how to find the numerator because I thought it would just be u, but wolfram alpha says it's u^3?

Dick
Homework Helper

## Homework Statement

$\int$(x^(1/3)/(x^(1/3)+1))dx

## Homework Equations

I know I have to use u substitution
u=x^(1/3)
du=1/(3x^(2/3))dx

## The Attempt at a Solution

I know that the denominator of the equation will be u+1, but I don't understand how to find the numerator because I thought it would just be u, but wolfram alpha says it's u^3?

If x^(1/3)=u then x^(2/3)=u^2. So du=(1/(3*u^2))dx. Does that tell you where the extra two powers of u are coming from?