InterviewSolution
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InterviewSolution
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`int(1)/(x^(2)-9)dx` is equal toA. `log|(x-3)/(x+3)|+C`B. `(1)/(6)log|(x-3)/(x+3)|+C`C. `(1)/(6)log|(x+3)/(x-3)|+C`D. `log|(x+3)/(x-3)|+C` |
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Answer» Correct Answer - B `int(1)/(x^(2)-9)dx=int(1)/(x^(2)-3^(2))dx=int(1)/((x+3)(x-3))dx` Let`" "(1)/((x+3)(x-3))=(A)/((x+3))+(B)/((x-3))` `" "1=A(x-3)+B(x+3)` `rArr" "1=x(A+B)+(-3A+3B)` On equation the coefficients of x and constant term on both sides, we get `A+B=0 and -3A+3B=1` On solving, we get `A=-(1)/(6) and B=(1)/(6)` `therefore int(1)/((x+3)(x-3))dx=int((-1))/(6(x+3))dx+int(1)/(6(x-3))dx` `=-(1)/(6)log|x+3|+(1)/(6)log|x-3|+C` `=(1)/(5)log|(x-3)/(x+3)|+C` |
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