Integrate the following w.r.t.x : log (x2 + 1) - Mathematics and Statistics

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Sum

Integrate the following w.r.t.x : log (x2 + 1)

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Solution

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

= `int [log (x^2 + 1)]*1dx`

= `[log(x^2 + 1)] int 1dx - int [d/dx{log (x^2 + 1)} int 1dx]*dx`

= `[log (x^2 + 1)]*x - int 1/(x^2 + 1)*dx (x^2 + 1)*xdx`

= `xlog(x^2 + 1) - int (2x^2)/(x^2 + 1)*dx`

= `xlog (x^2 + 1) - int (2x^2 + 2 - 2)/(x^2 + 1)*dx`

= `xlog(x^2 + 1) - int[(2(x^2 + 1))/(x^2 + 1) - 2/(x^2 + 1)]*dx`

= `xlog(x^2 + 1) - int[2 int 1dx - 2 int 1/(x^2 + 1)*dx]`

= x log (x2 + 1) – 2x + 2 tan–1 x + c.

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Chapter 3: Indefinite Integration - Miscellaneous Exercise 3 [Page 150]

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Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 3.12 | Page 150

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