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November 28th, 2011, 07:36 PM   #1
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Solving Indefinite Integral?

Hi guys, I was wondering how would you solve this equation:



I can already tell by u-subs it won't work and I don't remember learning how to solve problems like these in my calc homework or class.

I don't want an answer but can you give me a clue on how to solve a problem like this? I'd like to be able to know the concept well (:
Thank you!
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November 28th, 2011, 08:00 PM   #2
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Re: Solving Indefinite Integral?

We are given:



Let:

giving us:



Now the integration will be straightforward.
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November 28th, 2011, 08:09 PM   #3
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Re: Solving Indefinite Integral?

Quote:
Originally Posted by MarkFL
We are given:



Let:

giving us:



Now the integration will be straightforward.

Where did you get the from, Sir?
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November 28th, 2011, 08:12 PM   #4
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Re: Solving Indefinite Integral?

With solving for x gives:





Then replace x with this expression.
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November 28th, 2011, 08:15 PM   #5
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Re: Solving Indefinite Integral?

Quote:
Originally Posted by MarkFL
With solving for x gives:





Then replace x with this expression.

Ah, Thanks. My TA never told us we could do that -- I assumed he covered all the material on u-sub but I guess I was wrong. Thanks, Mark.
(:
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November 28th, 2011, 08:20 PM   #6
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Re: Solving Indefinite Integral?

Glad to help, and welcome to the forum!
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November 28th, 2011, 08:22 PM   #7
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Re: Solving Indefinite Integral?

Thanks !
I just hope I won't have a problem like this on my test this weekend, haha.
Wouldn't have thought of it this way at all xD.
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November 28th, 2011, 08:30 PM   #8
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Re: Solving Indefinite Integral?

Here's a slightly different way to look at it...

You have that x there and it needs to be replaced by an expression containing u, and you have said to let u = 2x - 1, so transform it like:

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November 29th, 2011, 06:28 AM   #9
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Alternatively, use integration by parts (if familiar with that method).
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November 29th, 2011, 08:47 AM   #10
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Re: Solving Indefinite Integral?

Hello, Jpyo!

Another approach . . .


Quote:

If the expression under the radical is linear,
[color=beige]. . [/color]we can let equal the entire radical.





[color=beige]. . . . . . . .[/color]




[color=beige]. . . . . . . . . . . . [/color]

[color=beige]. . . . . . . . . . . . [/color]

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