# Finding the integral of a function

## Homework Statement

Hi, all I need to do is find the integral of a function, and im struggling with where to begin with this particular expression.

## Homework Equations

$\int[(3x^2)/(x^3+ 2)]dx$

## The Attempt at a Solution

Thats the problem, im not sure where to start! Im sure it is something obvious I am missing.
Thanks

## The Attempt at a Solution

Last edited:

HallsofIvy
Homework Helper
I assume you mean $\int[(3x^2)/(x^3+ 2)]dx$.

Let $u= x^3+ 2$.

Thanks for your quick reply. Sorry, that is exactly what I meant, Im not great with laying stuff out online.

Substituting was my first thought, however this question is part of a pre-test Im doing for homework, and there is a section on substituting later on in the paper, so Im guessing I'm not supposed to use that here. Is there another way doing it?

For equations of this form, where the numerator is the derivative of the denominator, the integral is simply the natural logarithm of the denominator. So in this case it would be ln|x^3+2| + a constant of integration.

Mark44
Mentor
Substituting was my first thought, however this question is part of a pre-test Im doing for homework, and there is a section on substituting later on in the paper, so Im guessing I'm not supposed to use that here. Is there another way doing it?
Substitution is probably the easiest technique, and the one that should be tried first. I can't think of any other way to do this problem.

For equations of this form, where the numerator is the derivative of the denominator, the integral is simply the natural logarithm of the denominator. So in this case it would be ln|x^3+2| + a constant of integration.

I never knew that, that works every time? Care to explain how?

HallsofIvy
Because of "substitution" whether you call it that or not! If your integral is of the form $\int f'(x)/f(x)dx$, let u= f(x), du= f'dx changes the integral to $\int du/u$.