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Evaluate: int(x^2)/(x^6-a^6)dx...

Evaluate: `int(x^2)/(x^6-a^6)dx`

Text Solution

Verified by Experts

Let I = `int(x^2)/(x^6-a^6)dx`
= `int(x^2)/((x^3)^2-(a^3)^2)dx`
Let` x^3 = t , 3x^2 dx = dt`
Then,`1/3int(1)/((t)^2-(a^3)^2)dt`
=`(1/3)(1/(2 xx a^3))log((t-a^3)/(t+a^3))`
=`(1/6)(1 /a^3)log((x^3-a^3)/(x^3+a^3))`
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