InterviewSolution
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InterviewSolution
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`int[(sqrt(x^2+1)(ln(x^2+1)-2lnx)))/(x^4) dx`A. `((x^(2)+1)^(3//2))/(x^(3))[(2)/(3)-ln((x^(2)+1)/(x^(2)))]+C`B. `((x^(2)+1)^(3//2))/(3x^(3))[ln((x^(2)+1)/(x^(2)))-(2)/(3)]+C`C. `((x^(2)+1)^(3//2))/(3x^(3))[(2)/(3)-ln((x^(2)+1)/(x^(2)))]+C`D. `(sqrt(x^(2)+1))/(3x^(3))(ln.(x^(2)+1)/(x^(2))-(2)/(3))+C` |
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Answer» Correct Answer - C `I=int(sqrt(x^(2)+1).[ln(x^(2)+1)-2 In x])/(x^(4))dx` `=int sqrt(1+(1)/(x^(2))).(1)/(x^(3)).ln (1+(1)/(x^(2)))dx =-(1)/(2)int sqrt(t)` ln t dt on applying integration by parts, we get `=-(1)/(2)[ln t.(2t^(3//2))/(3)-int (1)/(t).(2)/(3)t^(3//2)dt]` `=-(1)/(3)t^(3//2)ln t +(2)/(9)t^(3//2)+C` `=((x^(2)+1)^(3//2))/(3x^(3)){(2)/(3)- ln((x^(2)+1)/(x^(2)))}+C` |
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