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December 26th, 2009, 02:07 PM   #1
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Integral u sub problem

Hi, I can't seem to get this problem to work out right...

? x(x+2)^1/2 dx

I let...

u=x+2
du=dx
x=u-2

So...

?(u-2)(u^1/2)du

=?u^3/2-2u^1/2 du
= (2/5)u^5/2 - 4/3u^3/2 +C

= 2/5(x+2)^5/2 - 4/3(x+2)^3/2 + C

But the book has it as...
[2/15(X+2)^3/2](3X-4) + C

It might just be a simplification issue, but I'm not so sure because the example in the book, which in the practice set referred me to, had an answer similar to mine. I think in the past I checked by differentiation and it didn't seem to work out anyway. Thanks.
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December 26th, 2009, 04:04 PM   #2
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Re: Integral u sub problem

Your answer and the book answer are equal. Just play with the algebra a little.
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December 26th, 2009, 06:02 PM   #3
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Re: Integral u sub problem

Hello, austen951!

Quote:

When given the square root of a linear expression,
[color=beige]. . [/color]I often let equal the entire radical.





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




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December 26th, 2009, 07:42 PM   #4
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Quote:
Originally Posted by austen951
I think in the past I checked by differentiation and it didn't seem to work out anyway.
Such a check should work, but a considerable amount of manipulation is sometimes required.

How would you tackle finding ??(x + 2x)dx (where x > -2)?
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December 31st, 2009, 01:04 PM   #5
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Re: Integral u sub problem

Thanks all. I got it now...I didn't find any errors in my work and didn't see how to manipulate to the books answer. I guess it's just a different approach.

And Skip I've never done an integral like that. I've only just finished a semester of Calc AB, and it seems over my head based on the integrals we've done.
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December 31st, 2009, 01:09 PM   #6
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Re: Integral u sub problem

Wait, I believe you can just factor out an x^2 and it becomes the same problem. hah
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December 31st, 2009, 01:40 PM   #7
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Re: Integral u sub problem

[quote 2/5(x+2)^5/2 - 4/3(x+2)^3/2 + C

But the book has it as...
[2/15(X+2)^3/2](3X-4) + C[/quote]

2/5(X+2)^5/2 = [2/5(X+2)^3/2](X+2)
therefore 2/5(x+2)^5/2 - 4/3(x+2)^3/2 + C = (X+2)^3/2[2/5(X+2) -4/3] + C

however [2/5(X+2) -4/3] = 2/15[3(X+2) - 10] = 2/15(3X - 4)

therefore your answer and book answer are the same!!!!!
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December 31st, 2009, 11:43 PM   #8
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Quote:
Originally Posted by austen951
it becomes the same problem.
Are you sure?
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January 1st, 2010, 01:37 AM   #9
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Re: Integral u sub problem

Actually no. I checked the graphs of both and I noticed an ever slight difference between sqrt (x^3-2x^2) and x sqrt(x-2).

Isn't it the same principle of say, reducing sqrt 28 to 2 sqrt 7? It seems like it, but I don't remember the rules for this at the moment...
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January 2nd, 2010, 03:49 AM   #10
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Do you have a textbook that explains this topic?
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