(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the integral. (Remember to use ln |u| where appropriate.)

∫(x^3 + 36)/(x^2 + 36)

2. Relevant equations

3. The attempt at a solution

A little bit confused about arriving at the solution for this problem. I get stuck a little ways in. Any help would be greatly appreciated!

First I divided x^3+36 by the denominator, since the power of the numerator is greater. Doing so, I got x + (-36x+36)/(x^2+36). I rewrote my integral as ∫ x + (-36x+36)/(x^2+36).

Now, I want to be able to use some facet of partial fractions, the whole A + B...etc, but I don't really see how I can in this case. If I split up the second half of the integral, I can write it as -36x/x^2+36 + 36/x^2+6^2. Applying b^2-4ac < 0, I know that I won't be able to factor and that I could complete the square in these cases, but I don't really see how that helps me either.

I don't think the problem calls for u-substitution, as I've tried that, and since the problem is part of the partial fractions section, I'm thinking they want us to go about using that method.

I'm not looking for an exact answer, just a little confused about what method to use from here.

Thanks in advance!

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# Homework Help: Integration of Rational Functions by Partial Fractions

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