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

ConceptMethods of Integration - Integration Using Partial Fractions

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

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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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