InterviewSolution
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InterviewSolution
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`int(1)/(x(1+root(3)(x))^(2))dx`is equal toA. `3{"log"((x^(1//3))/(1+x^(1//3)))+(1)/(1+root(3)(x))}+C`B. `3{"log"((x^(1//3))/(1+x^(1//3)))+(1)/(1+x^(1//3))}+C`C. `3{"log"((x^(1//3))/(1+x^(1//3)))-(1)/(1+x^(1//3))}+C`D. none of these |
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Answer» Correct Answer - a Let `I=int(1)/(x(1+root(3)(x))^(2))dx=int(1)/(t^(3)(1+t)^(2))3t^(2)dt` `rArr I=3int(1)/(t(t+1)^(2))dt=3 int{(1)/(t)-(1)/(t+1)-(1)/((t+1)^(2))}dt` `rArr I=3 { log_(e)t-log(t+1)+(1)/(t+1)}+C` `rArrI=3 {log_(e)((t)/(t+1))+(1)/(t+1)}+C` `rArrI=3{log_(e)(x^(1//3)/(1+x^(1//3)))+(1)/(x^(1//3)+1)}+C`. |
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