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Community Discussion Question: solve

Forum Index -> Integral Calculus

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15 May 2008 21:13:30 IST

Subject: solve

gokusuper (5)

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Olaaa!! Perrrfect answer.

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$\int$ (x⁴+a⁴)^-1 dx

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16 May 2008 11:37:27 IST

Subject: Re:solve

allamraju (3422)

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Olaaa!! Perrrfect answer.

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I=(1/2)(I₁-I₂) where I₁= $\int$ (x²+a²/x⁴+a⁴)dx= $\int$ 1+a²/x²/x²+a⁴/x².Now write denominator as (x-a²/x)²+2a² and put x-a²/x=t,It becomes $\int$ dt/t²+2a² which can be easily integrated.

Now,I₂= $\int$ (x²-a²/x⁴+a⁴)dx.Again divide nr and dr by x² and write dr. as (x+a²/x)²-2a².Now,Put t=x+a²/x,It becomes $\int$ dt/t²-2a² which is easy to integrate.

MAKING A MISTAKE IS HUMAN BUT REPEATING IT IS IDIOTIC.

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