InterviewSolution
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InterviewSolution
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The value of `int(x^(2)+1)/(x^(4)-x^(2)+1)dx` isA. `tan^(-1)(2x^(2)-1)+C`B. `tan^(-1)(x^(2)+1)/(x)+C`C. `sin^(-1)(x-(1)/(x))+C`D. `tan^(-1)((x^(2)-1)/(x))+C` |
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Answer» Correct Answer - D Let `l=int(x^(2)+1)/(x^(4)-x^(2)+1)dx=int(1+(1)/(x^(2)))/(x^(2)+(1)/(x^(2))-1)dx` `l=((1+(1)/(x^(2))))/((x-(1)/(x))^(2)+1)dx` `"Put "x-(1)/(x)=t rArr (1+(1)/(x^(2)))dx=dt` `therefore" "l=int(dt)/(t^(2)+1)tan^(-1)t+C = tan^(-1)(x-(1)/(x))+C` `=tan^(-1)((x^(2)-1)/(x))+C` |
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