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# Solution for Evaluate : ∫(1+logx)/(x(2+logx)(3+logx))dx - HSC Commerce (Marketing and Salesmanship) 12th Board Exam - Mathematics and Statistics

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ConceptIndefinite Integration Methods of Integration

#### Question

Evaluate : int (1+logx)/(x(2+logx)(3+logx))dx

#### Solution

Let I=int (1+logx)/(x(2+logx)(3+logx))dx

Put

logx=t

1/xdx=dt

I=int(1+t)/((2+t)(3+t))dt

consider

(1+t)/((2+t)(3+t))=A/(2+t)+B/(3+t)

(1+t)=A(3+t)+B(2+t)

A=-1,B=2

(1+t)/((2+t)(3+t))=-1/(2+t)+2/(3+t)

I=int-1/(2+t)dt+int2/(3+t)dt

=-log|(2+t)|+2log|(3+t)|+c

=log[|((3+t)^2)/(2+t)|] +c

=log[|(3+logx)^2/(2+logx)|]+C

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#### APPEARS IN

2014-2015 (March) (with solutions)
Question 3.2.1 | 4 marks

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Solution for question: Evaluate : ∫(1+logx)/(x(2+logx)(3+logx))dx concept: Indefinite Integration - Methods of Integration. For the courses HSC Commerce (Marketing and Salesmanship), HSC Commerce
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