InterviewSolution
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InterviewSolution
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`int(xdx)/((x-1)(x-2))` is equals toA. `log|((x-1)^(2))/(x-2)|+C`B. `log|((x-2)^(2))/(x-1)|+C`C. `log|((x-1)/(x-2))^(2)|+C`D. `log|(x-1)(x-2)|+C` |
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Answer» Correct Answer - B Let `(x)/((x-1)(x-2))=(A)/((x-1))+(B)/((x-2))` `rArr" "x=A(x-2)+B(x-1)" …(i)"` On substituting x = 1 in Eq (i), we get `A=-1` and on substituting x = 2 in eq (i), we get B = 2 `therefore " "(x)/((X-1)(x-2))=-(1)/((x-1))+(2)/((x-2))` `therefore int (x)/((x-1)(x-2))dx=int((-1))/(x-1)dx+int(2)/(x-2)dx` `=-log|x-1|+2log|x-2|+C` `=-log|x-1|+log(x-2)^(2)+C` `=log|((x-2)^(2))/(x-1)|+C` |
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