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Question Number 11619 by Nayon last updated on 29/Mar/17
Evaluate ∫(dx/((x+a)(x+b)))
Evaluate∫dx(x+a)(x+b)
Commented by Nayon last updated on 29/Mar/17
someone pls ans
someoneplsans
Answered by mrW1 last updated on 29/Mar/17
=(1/(a−b))ln ∣((x+b)/(x+a))∣+C
=1a−bln∣x+bx+a∣+C
Commented by mrW1 last updated on 29/Mar/17
(1/((x+a)(x+b))) =(p/(x+a))+(q/(x+b))=((px+pb+qx+qa)/((x+a)(x+b))) ⇒p+q=0 ⇒pb+qa=1 −p=q=(1/(a−b)) ∫(1/((x+a)(x+b)))dx =−(1/(a−b))∫(dx/(x+a))+(1/(a−b))∫(dx/(x+b)) =−(1/(a−b))ln ∣x+a∣+(1/(a−b))ln ∣x+b∣+C =(1/(a−b))ln ∣((x+b)/(x+a))∣+C
1(x+a)(x+b)=px+a+qx+b=px+pb+qx+qa(x+a)(x+b)⇒p+q=0⇒pb+qa=1−p=q=1a−b∫1(x+a)(x+b)dx=−1a−b∫dxx+a+1a−b∫dxx+b=−1a−bln∣x+a∣+1a−bln∣x+b∣+C=1a−bln∣x+bx+a∣+C

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