Integrate the following functions w.r.t. x : x2+2(x2+1).ax+tan-1x - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`

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Solution

Let I = `int (x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x).dx`

= `int a^(x + tan^-1x).((x^2 + 2)/(x^2 + 1)).dx`

Put x + tan–1x = t

∴ `(1 + 1/(1 + x^2)).dx` = dt

∴ `((1 + x^2 + 1)/(1 + x^2)).dx` = dt

∴ `((x^2 + 2)/(x^2 + 1)).dx` = dt

∴ I = `int a^t dt = a^t/loga + c`

= `(a^(x + tan^-1 x))/loga + c`.

  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Exercise 3.2 (A) [Page 110]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Exercise 3.2 (A) | Q 1.06 | Page 110

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