Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1 - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1 

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Solution

Let I = e3logx(x4 + 1)–1.dx

= `int e^(logx^3)/(x^4 + 1).dx`

= `int x^3/(x^4 + 1).dx`                         ...[∵ elogN = N]

= `(1)/(4) int(4x^3)/(x^4 + 1).dx`

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

= `(1)/(4)log|x^4 + 1| + 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 1.12 | Page 110

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