InterviewSolution
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InterviewSolution
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The value of `int(3x+2)/((x-2)^(2)(x-3))dx` is equal toA. `11log (x-3)/(x-2)-(8)/(x-2)+C`B. `11log (x+3)/(x+2)-(8)/(x-2)+C`C. `11log(x-3)/(x-2)+(8)/(x-2)+C`D. `11log (x+3)/(x+2)+(8)/(x-2)+C` |
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Answer» Correct Answer - C Let l`=int(3x+2)/((x-2)^(2)(x-3))dx" …(i)"` Again, let `(3x+2)/((x-2)^(2)(x-3))=(A)/((x-2))+(B)/((x-2)^(2))+(C)/((x-3))" …(ii)"` `rArr" "3x+2=A(x-2)(x-3)+B(x-3)+C(x-2)^(2)" ...(iii)"` On putting the values of `x=2,3` respectively, we get `3xx2+2=B(2-3)` `rArr B=-8` and `3xx3+2=C(3-2)^(2)` `rArr" "C=11` On equation the coefficient of `x^(2)` in Eq. (iii), we get `0=A+C" "rArr" "A=-11` On putting the values of A, B and C in Eq. (ii), we get `(3x+2)/((x-2)^(2)(x-3))=-(11)/((x-2))-(8)/((x-2)^(2))+(11)/((x-3))` `therefore" "l=int[-(11)/((x-2))-(8)/((x-2)^(2))+(11)/(x-3)]dx` `-11log(x-2)+(8)/((x-2))+11log(x-3)+C` `11log((x-3)/(x-2))+(8)/((x-2))+C` |
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