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## #1 2006-04-29 03:53:35

Simon
Guest

Hello everyone,

I am revising for my final exams and have come across these questions. I wonder if anyone can help me???

Evaluate the following using integration by parts.

∫x² + 1 /x² - 3x + 2

∫2x +3/ (x - 2)²

I would very much appreciate it if i could get help with these.

## #2 2006-04-29 13:30:48

renjer
Member
Registered: 2006-04-29
Posts: 50

Does it specifically state integration by parts? I think using partial fractions might be easier.

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## #3 2006-04-29 13:58:47

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

I don't think even partial fractions is needed.

For the first, you can just use the power rule.  For the second, use u substitution with u = x-2.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #4 2006-04-30 02:59:10

Simon
Guest

hi all,

thanks for that, but the answer specifically asks for integration by parts. I would be grateful if someone could give me a break down of how to do it.

Thanks

Simon

## #5 2006-05-01 01:42:41

renjer
Member
Registered: 2006-04-29
Posts: 50

That's the second problem done using integration by parts, it wasn't too bad (Add the constant at the end if you want). Trust me, you wouldn't want to use integration by parts for the first problem, it can get very messy.

Ricky wrote:

For the first, you can just use the power rule.

I don't really know how to use the "power rule" for the first problem.

Last edited by renjer (2006-05-01 01:45:05)

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## #6 2006-05-01 02:09:51

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

∫x² + 1 /x² - 3x + 2

By the power rule:

So:

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #7 2006-05-01 02:22:06

George,Y
Member
Registered: 2006-03-12
Posts: 1,306