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**1. The problem**

Find the definite integral.

[tex]\int \frac {t^2 - 3}{-t^3 + 9t + 1} dt[/tex]

**2. The attempt at a solution**

The answer is the book made it seem like the rule [itex] \int \frac {du}{u} = ln|u| + C [/itex] was used. Here's what I got:

[tex]u = -t^3 + 9t + 1[/tex]

[tex]du = -3t^2 + 9\;dt[/tex]

[tex]-\frac{1}{3}du = t^2 + 9\;dt[/tex]

Obviously this won't work out, so is there something I'm overlooking that anyone can point out?

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