InterviewSolution
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InterviewSolution
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The value of the integral `int(dx)/(x^(n)(1+x^(n))^(1//n)), n in N` isA. `(1)/((1-n))(1+(1)/(x^(n)))^(1-1//n)+C`B. `(1)/((1-n))(1-(1)/(x^(n)))^(1-1//n)+C`C. `(1)/((1-n))(1-(1)/(x^(n)))^(1-1//n)+C`D. `(1)/((1-n))(1-(1)/(x^(n)))^(1-1//n)+C` |
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Answer» Correct Answer - A `int(dx)/(x^(n)(1+x^(n))^(1//n))=int(dx)/(x^(n).x((1)/(x^(n))+1)^(1//n))` `=int(dx)/(x^(n+1)((1)/(x^(n))+1)^(1//n))` `"Put "(1)/(x^(n))+1=t` `rArr-(n)/(x^(n+1))dx=dt` `rArr" "-(1)/(n)int(dt)/(t^(1//n))=-(1)/(n)int t^(-1//n)dt=-(1)/(n).(t^(1-(1)/(n)))/((1-(1)/(n)))+C` `=(1)/((1-n))(1+(1)/(x^(n)))^(1-(1)/(n))+C` |
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