# Thread: I'm not sure how to take the antiderivative of a fraction

1. ## I'm not sure how to take the antiderivative of a fraction

How do you take an antiderivative of a fraction for example 1/(t^3-1).

On a side note, where can I find info on using the [MATH /MATH] tags.

2. Originally Posted by swatpup32
How do you take an antiderivative of a fraction for example 1/(t^3-1).
first use the difference of two cubes formula to get

$\int \frac 1{t^3 - 1}~dt = \int \frac 1{(t - 1)(t^2 + t + 1)}~dt$

now use partial fractions

On a side note, where can I find info on using the [MATH /MATH] tags.
see the last link in my signature.

3. And in case it isn't clear, I should point out that there is no simple formula for finding the antiderivative of any general rational function. Some such functions will not even have elementary antiderivatives. It all depends on exactly what the fraction consists of.

This is characteristic of integration in general. With differentiation, you can find the derivative of any elementary function (if it exists) by using the sheer mechanical application of some straightforward rules. With integration, this is not so.

For the antiderivative of your specific expression, follow Jhevon's suggestion and use partial fraction decomposition.