InterviewSolution
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InterviewSolution
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The value of `int(1)/(x+sqrt(x-1))dx`, isA. `log(x+sqrt(x-1))+sin^(-1)(sqrt((x-1)/(x)))+C`B. `log(x+sqrt(x-1))+C`C. `log(x+sqrt(x-1))-(2)/(sqrt3)tan^(-1)((2sqrt(x-1)+1)/(sqrt3))+C`D. None of the above |
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Answer» Correct Answer - C Let `l=int(dx)/(x+sqrt(x-1))` Put`" "x=t^(2)+1 rArr dx=2tdt` `therefore" "l=int(2t)/(t^(2)+t+1)dt=int(2t+1)/(t^(2)+t+1)dt-int(1)/(t^(2)+t+1)dt` `=log(t^(2)+t+1)-int(1)/((t+(1)/(2))^(2)+((sqrt3)/(2))^(2))dt` `=log(t^(2)+t+1)-(2)/(sqrt3)tan^(-1)((2t+1)/(sqrt3))` `=log(x+sqrt(x-1))-(2)/(sqrt3)tan^(-1)((2sqrt(x-1)+1)/(sqrt3))+C` |
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