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[Post New]15 Mar 2008 19:14:08 IST
    Subject: Re:Integrals challenge 1
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elastiboysai (2327)

Blazing goIITian

Olaaa!! Perrrfect answer. 421  [532 rates]
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Hi guyz
Razz
I just found anoder interesting method 2 solv it.. widout Euler's substitution.



P = \int \frac{x}{(7x - 10 - x^2)^{3/2}}\,dx = \int \frac{x}{\left[\frac{9}{4} - \left(x - \frac{7}{2}\right)^2\right]^{3/2}}\,dx,

and now we are to make the substitution x - \frac{7}{2} = \frac{3}{2} \sin t: the result is

P = \int \frac{\frac{3}{2} \sin t + \frac{7}{2}}{\left(\frac{9}{4} - \frac{9}{4} \sin^2t\right)} \cdot \frac{3}{2} \cos t\,dt = \frac{2}{9}\int (3 \cos^{-2}t \sin t + 7 \sec^2t)\,dt

and you can finish from here.Very Happy
 this reply: 19 points  (with 3 Olaaa!! Perrrfect answer.   in 5 votes )   [?]
 
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