HSC Arts 12th Board ExamMaharashtra State Board
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Solution for Evaluate : ∫(x+1)/((x+2)(x+3))dx - HSC Arts 12th Board Exam - Mathematics and Statistics

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Question

Evaluate : `∫(x+1)/((x+2)(x+3))dx`

Solution

Let I=`∫(x+1)/((x+2)(x+3))dx`

`(x+1)/((x+2)(x+3))=A/(x+2)+B/(x+3)`

`x+1=A(x+3)+B(x+2)`  .........(i)

∴ Putting x = -2 in equation (i) we get

-1 = A
∴ A = -1
∴ Putting x = -3 in equation (i) we get
-2 = -B
∴ B = 2

∴(x+1)/((x+2)(x+3))=1/(x+2)+2/(x+3)

`∴ I=int[-1/(x+2)+2/(x+3)]dx`

`∴I=-log|x+2|+2log|x+3|+c`

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APPEARS IN

 2015-2016 (July) (with solutions)
Question 4.2.2 | 2.00 marks
Solution for question: Evaluate : ∫(x+1)/((x+2)(x+3))dx concept: Methods of Integration - Integration Using Partial Fractions. For the courses HSC Arts, HSC Science (Electronics), HSC Science (General) , HSC Science (Computer Science)
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