Polynomial indefinite integral

• Jun 25th 2012, 09:51 AM
Ragnarok
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?
• Jun 25th 2012, 09:57 AM
Plato
Re: Polynomial indefinite integral
Quote:

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 $\int \frac{t^2-3}{-t^3+9t+1}dt=\frac{-1}{3}\int \frac{-3t^2+9}{-t^3+9t+1}dt$
• Jun 25th 2012, 11:01 AM
Ragnarok
Re: Polynomial indefinite integral
Thanks! But I still don't get it. How does that help?
• Jun 25th 2012, 11:03 AM
Ragnarok
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?
• Jun 25th 2012, 09:13 PM
Prove It
Re: Polynomial indefinite integral
Quote:

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.
• Jun 25th 2012, 10:45 PM
richard1234
Re: Polynomial indefinite integral
Let $u = -t^3 + 9t + 1$. What is du/dx?