Calculus - Indefinite Integral (2):

1

pandit ·2010-12-22 07:48:27

\int \frac{(1-\frac{1}{x^2})dx}{(\sqrt{x+\frac{1}{x}+\alpha})(\sqrt{x+\frac{1}{x}+\beta})}

put x+\frac{1}{x}=t and u r done

answer is

\ln{\left( \frac{2(\sqrt{x^2+\alpha x+1)(x^2+\beta x +1)}}{x}+\alpha+\beta+2x\right)}+K

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1

Ricky ·2010-12-22 07:54:38

I ' ll outline a proof - you will be able to solve then I hope -

Take out an " x " each from the two square roots . You will be left with a " x ² " in the denominator and the two square roots . Then , divide the numerator by " x² " . Here , write " x + 1x = z " . You will get " dz " on the numerator only , and you ' ll also be left with a standard integral .

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1708

man111 singh ·2010-12-24 07:52:39

Yes pandit and Ricky both u are Right.

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souradeepmajumde majumder ·2010-12-24 10:22:37

BOTH ARE RIGHT.

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