InterviewSolution
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InterviewSolution
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`int(x^(2))/((x^(2)+4)(x^(2)+9))dx` का मान ज्ञात कीजिए । |
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Answer» `int(x^(2))/((x^(2)+4)(x^(2)+9))dx` माना `x^(2)=y` तथा आंशिक भिन्नों में व्यक्त करने पर ltbgt `(y)/((y+4)(y+9))=(A)/((y+4))+(B)/((y+9))" …(1)"` `y=A(y+9)+B(y+4)` यदि `" "y=-4," तब "A=-(4)/(5)` और यदि `" "y=-9," तब "B=(9)/(5)` अब समीकरण (1 ) से `(y)/((y+4)(y+9))=(-4)/(5(y+4))+(9)/(5(y+9))` `rArr" "(x^(2))/((x^(2)+4)(x^(2)+9))=(-4)/(5(x^(2)+4))+(9)/(5(x^(2)+9))` `rArr int (x^(2))/((x^(2)+4)(x^(2)+9))dx=-(4)/(5)int(1)/((x^(2)+4))dx+(9)/(5)int(1)/((x^(2)+9))dx` `=-(4)/(5)tan^(-1).(x)/(2).(1)/(2)+(9)/(5)tan^(-1).(x)/(3).(1)/(3)+c` `=-(2)/(5)tan^(-1).(x)/(2)+(3)/(5)tan^(-1).(x)/(3)+c` |
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