Integrate the following functions w.r.t. x : 14x+5x-11 - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`

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Solution

Let I = `int(1)/(4x + 5x^-11).dx`

= `int x_11/(x^11(4x + 5x^-11)).dx`

= `int x^11/(4x^12 + 5).dx`

= `(1)/(48) int(48x^11)/(4x^12 + 5).dx`

= `(1)/(48) int(d/dx(4x^12 + 5))/(4x^12 + 5).dx`

= `(1)/(48)log|4x^12 + 5| + c     ...[∵ int (f'(x))/f(x) dx = log|f(x)| + c]`

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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 1.1 | Page 110

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