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Integrate the following functions x^2/(1...

Integrate the following functions `x^2/(1-x^6)`

Text Solution

Verified by Experts

Let t = `x^3`. Then dt = `3x^2 dx`
`gt x^2 dx = 1/3 dt`
therefore` int x^2/(1-x^6) dx = int x^2/(1-(x^2)^3) dx`
= `int 1/(1-t^2) 1/3 dt`
=`1/3 xx 1/2 log |(1+t)/(1-t)|+c`
=`1/6 log|(1+x^3)/(1-x^3)|+c`
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