InterviewSolution
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InterviewSolution
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`"If"int(dx)/(x^(3)(1+x^(6))^(23))=xf(x)(1+x^(6))^(1/3)+C` where, C is a constant of integration, then the function f(x) is equal toA. `-(1)/(2)`B. `-(1)/(6)`C. `-(6)/(x)`D. `-(x)/(2)` |
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Answer» Correct Answer - a Let `=int(1)/(x^(3)(1+x^(6))^(2//3))dx` . Then `I=int(1)/(7(1+(1)/(x^(6)))^(2//3))dx=-(1)/(6)int(1+(1)/(x^(6)))^(-2//3)d(1+(1)/(x^(6)))` `rArrI=-(1)/(2)(1+(1)/(x^(6)))^(1//3)+C` `rArrf(x)(1+x^(-6))^(1//3)+C=-(1)/(2)(1+x^(-6))^(1//3)+C` `rArrf(x)=-(1)/(2)`. |
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