InterviewSolution
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InterviewSolution
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`int(1)/(xsqrt(1-x^(3)))`dx is equal toA. `(1)/(3)log|(sqrt(1-x^(3)-1))/(sqrt(1-x^(3))+1)|+C`B. `(1)/(2)log|(sqrt(1-x^(2))+1)/(sqrt1-x^(2))-1|+C`C. `(1)/(3)log|(1)/(sqrt(1-x^(3)))|+C`D. none of these |
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Answer» Correct Answer - a We have , `I=int(1)/(xsqrt(1-x^(3)))dx` `rArrI=-(1)/(3)int(1)/(x^(3)sqrt(1-x^(3)))(-3x^(2))dx` `rArrI=-(1)/(3)int(1)/(x^(3)sqrt(1-x^(3)))(1-x^(3))dx` `rArrI=-(1)/(3)int(1)/((1-t^(2))sqrt(t^(2)))` 2t dt , where `t^(2)=1-x^(3)` `rArrI=-(2)/(3)int(1)/(1-t^(2))dt=(2)/(3)int(1)/(t^(2)-1^(2))dt=(1)/(3)log|(t-1)/(t+1)|+C` `rArrI=(1)/(3)log|(sqrt(1-x^(3))-1)/(sqrt(1-x^(3))+1)|+C` |
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