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Evaluate the integral

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Anonymous

Expert

Karma Points: 1,179

Date Posted: 7/23/2008 6:16:47 PM Status: Live

Asker's Rating: Lifesaver

Response:

split the integral

Altair

Oracle

Karma Points: 12,414

Date Posted: 7/23/2008 6:32:52 PM Status: Live

Asker's Rating: Helpful

Response:

Don't forget give me good rating to show your respect for my time to help you!

leettab

Sage

Karma Points: 5,311

Date Posted: 7/23/2008 6:34:41 PM Status: Live

Asker's Rating: Helpful

Response:

Let

then

Now make the substitution into the integral

integrating we get

now we have to back substitute

we can simplify further

you get the same answer using trig substitution as you do when using partial fraction decomposition

frozenfire017

Expert

Karma Points: 1,051

Date Posted: 7/23/2008 7:01:42 PM Status: Live

Asker's Rating: Helpful

Response:

Okay so here is our problem below. First off we try the substitution rule and find that it does not work.

We then see that we can brake up this problem into two separate integrals just by knowing common algebra rules.

With this we can now use the substitution rule on the first integral and trigonometry properties on the second integral.

So first integral (one with 2x):

let u =

du = 2xdx

-> dx = du/2x

Plug in for dx now:

So...

Now for the second integral (1 instead of 2x as numerator):

We can't use substitution rule so we look at trig rules.

And...

So...

Our final answer is:

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Evaluate the integral

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