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Evaluate: int(xtan^(-1)x^2)/(1+x^4)dx...

Evaluate: `int(xtan^(-1)x^2)/(1+x^4)dx`

Text Solution

Verified by Experts

Let`x^2=t`
`xdx=dt/2`
Thus,`int(xtan^(-1)x^2)dx` =`int(tan^(-1)t)dt/2`
=`1/2[tan^(-1)t t -int(t/(1+x^2)dt]`
Let `1+t^2=a`
`2tdx=da`
or,`1/2[tan^(-1)t t -int((da)/(2a))`
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