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Integral Calculus

New kid on the Block

 Joined: 8 Nov 2006 Post: 3
10 Nov 2006 19:26:36 IST
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indefinate int.
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Integral Calculus

1/(cos3x - sin3x)

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Joined: 19 Oct 2006
Posts: 1558
22 Jun 2007 20:30:33 IST
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hmmm... puneet, amar, bipin??? no iit dudes ready to verify this one? i guess our pal mr iitian has been upto something? :)

Hot goIITian

Joined: 25 Jan 2007
Posts: 154
22 Jun 2007 21:52:21 IST
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for sure the question is a great one...
and yes Lois , for sure its integrable...
to solve this a person must have a good knowledge of polylogarithmic functions and yes, not to to forget a lot of patience,a lot....it reguire a lot of heart to get solving it...........
But not many would have read about it i suppose....thats the reason they think it to be non integrable...
MR.IITIAN007 is correct in his approach.......
and yes, i tried to solve it and its soluton is of about 8 pages,with its final answer ,without limits to be of 15 lines itself...
its quite tough and time consuming...lois ,i suggest you don't heck your head  too much at it...it holds less imp. but, do get to study polylogarithmic function, inverse hyperbolic functions...just for a little interest..
and heres what i 'm getting just don't get scared........

and yes..i have checked it with the integrator...I was correct...

I myself cannot write  it all out here its time consuming(as my typing speed is too low) so, get to..."the wolfram integrator" its reliable..but a few of the expressions in its sollution can be simplified..just have a look..

Cool goIITian

Joined: 24 May 2007
Posts: 39
24 Jun 2007 01:37:43 IST
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Wow what an answer Ken. So you have completed studying pollylogarithmic functions also ??? Impressive ! ! ! !

New kid on the Block

Joined: 1 Jul 2007
Posts: 18
1 Jul 2007 19:22:03 IST
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denominator is = (cosx-sinx)(1+sin2x)
put cosx+sinx=t
(cosx-sinx)dx=dt
t^2=1+sin2x, sin2x=1-t^2;

integral{dt/((cosx-sinx)^2*(1+sin2x)=dt/(1-sin2x)*(1+sin2x)

dt/(2-t^2)*(t^2)

split it up into 2 integrals by partial fractions solve

Blazing goIITian

Joined: 17 Oct 2007
Posts: 1659
15 Feb 2009 17:57:02 IST
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So what's the answer finally to Lois question?

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