1. ## Polynomial indefinite integral

Hello, I'm in calculus 2 and have this problem:

$\int \frac{t^2-3}{-t^3+9t+1}dt$

Separating the numerator does not seem to do any good. How should I proceed?

2. ## Re: Polynomial indefinite integral

Originally Posted by Ragnarok
Hello, I'm in calculus 2 and have this problem:

$\int \frac{t^2-3}{-t^3+9t+1}dt$
Note that $\int \frac{t^2-3}{-t^3+9t+1}dt=\frac{-1}{3}\int \frac{-3t^2+9}{-t^3+9t+1}dt$

3. ## Re: Polynomial indefinite integral

Thanks! But I still don't get it. How does that help?

4. ## Re: Polynomial indefinite integral

Okay, never mind, I got it. So the point here was that we needed to make the numerator something that would cancel out the derivative of the denominator?

5. ## Re: Polynomial indefinite integral

Originally Posted by Ragnarok
Okay, never mind, I got it. So the point here was that we needed to make the numerator something that would cancel out the derivative of the denominator?
Yes. The moral of the story, always look for an "inner" function with its derivative as a multiple, then you can use a substitution.

6. ## Re: Polynomial indefinite integral

Let $u = -t^3 + 9t + 1$. What is du/dx?