Maharashtra State BoardHSC Arts 12th Board Exam
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Integrate the following w.r.t. x: (1+logx)2x - Mathematics and Statistics

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Sum

Integrate the following w.r.t. x: `(1 + log x)^2/x`

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Solution

Let I = `int (1 + log x)^2/x*dx`

Put 1 + log x = t

∴ `(1)/x*dx` = dt

∴ I = `int t^3*dt = (1)/(4)t^4 + c`

= `(1)/(4)(1 + logx)^4 + c`.

Concept: Methods of Integration: Integration by Parts
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 3.01 | Page 150

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