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 Q6  Integrate the functions \frac{x ^ 2 }{1- x ^ 6 }

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\frac{x ^ 2 }{1- x ^ 6 }

let x^3 =t
then 3x^2dx =dt

using the special identities we can simplify the integral as follows

\int \frac{x^2}{1-x^6}dx =\frac{1}{3}\int \frac{dt}{1-t^2}
                           =\frac{1}{3}[\frac{1}{2}\log\left | \frac{1+t}{1-t} \right |]+C\\ =\frac{1}{6}\log\left | \frac{1+x^3}{1-x^3} \right |+C

Posted by

manish

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