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Evaluate int (xtan^(-1)x)/(1+x^2)^(3/2) ...

Evaluate `int (xtan^(-1)x)/(1+x^2)^(3/2) dx`

Text Solution

Verified by Experts

`Let x=tantheta`
`dx=sec^2d theta`
`1+x^2=1+tan^2theta=sec^2theta`
`int(xtan^(-1)xdx)/(1+x^2)^(3/2)`
`int(tantheta*theta*sec^2theta*dthet a)/(sec^2theta)^(3/2)`
`inttheta*tantheta*sec^2theta/sec^3theta dthet a`
`inttheta*sinthetad theta`
`-thetacostheta+sintheta+c`
...
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