InterviewSolution
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InterviewSolution
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`(2x-3)/((x^(2)-1)(2x+3))` |
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Answer» `int(2x-3)/((x^(2)-1)(2x+3))dx` `" "=int(2x-3)/((x-1)(x+1)(2x+3))dx` माना `" "(2x-3)/((x-1)(x+1)(2x+3))=(A)/((x-1))+(B)/((x+1))+(C)/((2x+3))` `rArr" "(2x-3)/((x-1)(x+1)(2x+3))` `" "(A(2x+3)(x+1)+B(x-1)(2x+3)+C(x-1)(x+1))/((x-1)(x+1)(2x+3))` `rArr 2x-3=A(2x+3)(x+1)+B(x-1)(2x+3)+C(x-1)(x+1)` `{:(x=1,"तो ",2-3=A(5)(2)+0+0,rArr.,A=-(1)/(10)),(x=-1,"तो ",-2-3=0+B(-2)(1)+0,rArr.,B=(5)/(2)):}` `rArr x=-(3)/(2)" तो "-3-3=0+0+C(-(5)/(2))(-(1)/(2))` `rArr C=-(24)/(5)` `therefore" "A=-(1)/(10), B=(5)/(2)" तथा "C=-(24)/(5)` `therefore" "int(2x-3)/((x^(2)-1)(2x+3))dx` `" "=int((-1))/(10(x-1))dx+(5)/(2)int(1)/(x+1)dx-(24)/(5)int(1)/(2x+3)dx` `=-(1)/(10)log|x-1|+(5)/(2)log|x+1|-(24)/(5)(log|2x+3|)/(2)+C_(1)` `=(5)/(2)log|x+1|-(1)/(10)log|x-1|-(12)/(5)log|2x+3|+C_(1)` |
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