InterviewSolution
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InterviewSolution
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`int(2)/((2-x)^(2))root3((2-x)/(2+x))dx` is equal toA. `(4)/(3)((2+x)/(2-x))^(2//3)+C`B. `(3)/(4)((2+x)/(2-x))^(2//3)+C`C. `(3)/(4)((2-x)/(2+x))^(2//3)`D. `(3)/(4)((2+x)/(2-x))^(4//3)+C` |
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Answer» Correct Answer - B Put `(2-x)/(2+x)=z^(3) rArr x=(2-2z^(3))/(1+z^(3))` `rArr" "dx=(-12z^(2)dz)/((1+z^(3))^(2))` `therefore" "int(2)/((2-x)^(2)) root3((2-x)/(2+x))dx` `=int(2)/([2-(2-2z^(3))/(1+z^(3))]^(2)).z.((-12z^(3)))/((1+z^(3))^(2))dz` `=(-3)/(2)int(dz)/(z^(3))=(3)/(4z^(2))+C=(3)/(4)((2+x)/(2-x))^(2//3)+C` |
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