InterviewSolution
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InterviewSolution
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`int{(logx-1)/(1+(logx)^(2))}^(2)` dx is equal toA. `(x)/((logx)^(2)+1)+C`B. `(xe^(x))/(1+x^(2))+C`C. `(x)/(1+x^(2))+C`D. `(logx)/((logx)^(2)+1)+C` |
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Answer» Correct Answer - a We have , `I=int{(logx-1)/(1+(logx)^(2))}^(2)dx` `rArr I=inte^(t)((t-1)^(1))/((t^(2)+1)^(2))dt` , where t = log x `rArrI=inte^(t)(t^(2)+1-2t)/((t^(2)+1)^(2))dt` `rArr I=inte^(t){(1)/(underset(f)(t^(2)+1))+(-2t)/(underset(f)((t^(2)+1)^(2)))}dt` `rArrI=(e^(t))/(t^(2)+1)+C=(x)/((logx)^(2)+1)+C` |
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