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Evalaute: int((logx-1)/(1+(logx)^2))^2dx...

Evalaute: `int((logx-1)/(1+(logx)^2))^2dx`

Text Solution

Verified by Experts

The correct Answer is:
`(x)/(1+(logx)^(2))+C`
` "Put " log x=t, "i.e.," x=e^(t) " so that " dx=e^(t) dt`
`:. int(((t-1))/(1+t^(2)))^(2)e^(t)dt=int e^(t)[(1)/(1+t^(2))-(2t)/((1+t^(2))^(2))]dt `
`=e^(t)(1)/(1+t^(2))+C`
`=(x)/(1+(logx)^(2))+C`
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