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Evaluate : int(xlog(e)x)/((x^(2)-1)^(3//...

Evaluate : `int(xlog_(e)x)/((x^(2)-1)^(3//2))dx`

Text Solution

Verified by Experts

The correct Answer is:
`(-log_(e)x)/(sqrt(x^(2)-1))+sec^(-1)x+C`
`int(xlog_(e)x)/((x^(2)-1)^(3//2))dx`
`=log_(e)x int(x)/((x^(2)-1)^(3//2))dx-int((1)/(x)(int(x)/((x^(2)-1))^(3//2)))dx`
`=(-log_(e)x)/(sqrt(x^(2)-1))+int(1)/(xsqrt(x^(2)-1))dx`
`=(-log_(e)x)/(sqrt(x^(2)-1))+sec^(-1)x+C`
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