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 Post subject: IntegralPosted: Mon, 8 Sep 2008 14:02:12 UTC
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Joined: Sat, 20 Oct 2007 18:26:04 UTC
Posts: 385
Here's one for y'all:

Hint:
Spoiler:

I *think* I have the answer, let's see if anyone agrees:
Spoiler:

Last edited by Tommo on Mon, 8 Sep 2008 19:49:50 UTC, edited 1 time in total.

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 Post subject: Posted: Mon, 8 Sep 2008 15:35:28 UTC
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Is |k| < 1?

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 Post subject: Posted: Mon, 8 Sep 2008 15:52:27 UTC
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Assuming my answer is correct (it may very well be wrong), it seems like it will have to be, if it is to be real. I hadn't thought about placing such a restriction initially though. Dunno

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 Post subject: Re: IntegralPosted: Mon, 8 Sep 2008 16:47:34 UTC
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Joined: Mon, 19 May 2003 19:55:19 UTC
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Location: Lexington, MA
Hello, Tommo!

My answer's slightly different . . .

Quote:

Substitute: .

Complete the square: .

Integrate: .

Back-substitute: .

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 Post subject: Posted: Mon, 8 Sep 2008 18:11:57 UTC
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Ah, nice solution Soroban.

I agree with you up to

Then for some reason I divided everything by as I had an 'arctanh()' in mind for my final answer.

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 Post subject: Posted: Wed, 15 Oct 2008 23:03:50 UTC
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Joined: Thu, 11 Sep 2008 01:59:14 UTC
Posts: 73
[url][URL=http://imageshack.us][/url]
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 Post subject: Posted: Tue, 21 Oct 2008 00:38:57 UTC
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Joined: Thu, 11 Sep 2008 01:59:14 UTC
Posts: 73
From my previous post, I find.

(x/k) - ln |csc(x)+cot(x)| + C , k ε R - {0}

Verification:

d/dx [(x/k) - ln |csc(x)+cot(x)| + C ]

= 1 / (k+sinx)

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