Find the indefinite integral of the function:

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- March 2nd 2009, 09:20 AMMy Little PonyRational Function Integration
Find the indefinite integral of the function:

- March 2nd 2009, 09:29 AMJameson
Doing this on Mathematica shows the answer has three separate terms which makes me think that partial fractions will be involved. I would try factoring the denominator and see where that leads.

- March 2nd 2009, 10:15 AMredsoxfan325
Start with partial fractions.

The denominator factors to: .

Thus you have .

Partial fractions:

Eliminating the denominators yields .

Multiplying this out gives .

Set , , and .

This makes , , and .

Thus you integral becomes . (I completed the square in the denominator of the second integral.)

The first integral clearly equals .

From now on, I'll be dealing only with the second integral.

Rewrite it like this: .

Now, break it up into two integrals: .

In the first integral, let . Thus . Now that integral becomes .

On the second integral, factor out the and complete the square in the denominator to get .

Then, factor a out of the denominator to get: .

Rewrite the denominator: .

Let and .

Thus your integral becomes: .

Factor out the and you have .

Adding all the parts together gives you: .

Thus: .