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Integral Calculus

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30 Oct 2007 08:59:09 IST

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467

dx/(sin^3x +cos^3x)

None

integrate

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ajit bothra

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Joined: 30 Oct 2007

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30 Oct 2007 09:00:12 IST

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integrate dx/(sin^3x+cos^3x)

puneet

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Joined: 19 Oct 2006

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7 Nov 2007 02:36:50 IST

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hey

use a^3 + b^3 = (a+b)(a^2 + b^2 -a.b)

Make partial fractions and then both parts are easily integrable ..

cheers

astrojith

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8 Nov 2007 19:20:50 IST

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Is the method you suggested be used in higher degrees ? I mean, in

dx/sin⁵x+cos⁵x and all ?

Would appreciate some more explanation.

richa sharma

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8 Nov 2007 19:27:43 IST

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@ puneet

how to make partial fractions in this case i cant understand since there is an a.b term present

i can think of this soln right now...divide by cos³x, substitute for the denominator....finally use partial fraction expansion and then integ by parts.....anyone plz suggest a shorter method...and plz tell the complete soln

Shankar Sengupta

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9 Nov 2007 17:41:35 IST

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Use this. You'll get the answer.
(sin x)^3= (3sinx-sin3x)/4. (cos x)^3=(cos 3x+ 3cos x)/4.

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