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`int_(1)^(e){((logx-1))/(1+(logx)^(2))}^(2)`dx is equal toA. `e/2`B. `1/2`C. `(e-2)/2`D. None of these |
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Answer» Correct Answer - 3 `I=underset(1)overset(e)int[((logx-1))/(1+(log)^(2))]^(2)dx` put log x=t`rArrx=e^(t)` `dx=e^(1)dt` `I=underset(0)overset(1)inte^(1){(t-1)/(1-t^(2))}^(2)dt` `=underset(0)overset(1)inte^(t)[1/(1+t^(2))-(2t)/(1+t^(2))^(2)}dt` `=[(e^(1))/(1+t^(2))]_(0)^(1)=e/2-1=(e-2)/2` |
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