InterviewSolution
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InterviewSolution
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`int(1)/(xsqrt(1-x^(3)))`dx is equal toA. `(1)/(3)log((1)/(sqrt(1-x^(3))))+C`B. `(2)/(3)log((1)/(sqrt(1-x^(3))))+C`C. `(1)/(3)log((sqrt(1-x^(3))-3)/(sqrt(1-x^(3)+3)))+C`D. `(1)/(3)log((sqrt(1-x^(3))-3)/(sqrt(1-x^(3))+1))+C` |
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Answer» Correct Answer - D `l=(dx)/(xsqrt(1-x)^(3))` On multiplying numerator and denominator by `x^(2)`, we get `l=int(x^(2)dx)/(x^(3)sqrt(1-x^(3)))` On putting `1-x^(3)=t^(2)=t = sqrt(1-x^(3))` `rArr" "-3x^(2)dx=2t dt` `rArr" "x^(2)dx=-(2)/(3)t dt and x^(3)=1-t^(2)` `therefore" "l=-(2)/(3)int(tdt)/((1-t^(2))t)` `=(2)/(3)int(dt)/(t^(2)-1)=(2)/(3)[(1)/(2)log|(t-1)/(t+1)|]+C` `=(1)/(3)log|(t-1)/(t+1)|+C` `=(1)/(3)log|(sqrt(1-x^(3))-1)/(sqrt(1-x^(3))+1|+C` |
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