InterviewSolution
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InterviewSolution
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`(5x)/((x+1)(x^(2)+9))` |
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Answer» `int(5x)/((x+1)(x^(2)+9))dx` माना `(5x)/((x+1)(x^(2)+9))=(A)/(x+1)+(Bx+C)/(x^(2)+9)` `rArr" "5x=A(x^(2)+9)+(Bx+C)(x+1)` `x=-1` तो `-5=A(1+9)+0rArr A=-(1)/(2)` `x=0` तो `0=9A+C" "rArr" "C=(9)/(2)` `x^(2)` के गुणांकों को बराबर, `A+B=0` `rArr" "B=-A=(1)/(2)` `thereforeint(5x)/((x+1)(x^(2)+9))dx=int((-(1)/(2)))/((x+1))dx+int((1)/(2)x+(9)/(2))/(x^(2)+9)dx` `" "=-(1)/(2)int(1)/(x+1)dx+(1)/(2)int((x+9)/(x^(2)+9))dx` `" "=-(1)/(2)log|x+1|+(1)/(2).(1)/(2)int(2x)/(x^(2)+9)dx+(9)/(2)int(1)/(x^(2)+9)dx` `" "=-(1)/(2)log|x+1|+(1)/(4)log|x^(2)+9|+(9)/(2).(1)/(3)tan^(-1)((x)/(3))+C` `" "=-(1)/(2)log|x+1|+(1)/(4)log|x^(2)+9|+(3)/(2)tan^(-1)((x)/(3))+C` |
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