Evaluate the following : ∫13x2+5x+7.dx - Mathematics and Statistics

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Sum

Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`

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Solution

I = `int1/sqrt(3x^2 + 5x + 7)dx`

I = `1/sqrt3 int 1/sqrt(x^2 + (5x)/3 + 7/3)dx`

I = `1/sqrt3 int 1/sqrt((x^2 + (5x)/3 + 25/36) + (7/3 - 25/36))dx`

I = `1/sqrt3 int 1/sqrt((x^2 + (5x)/3 + (5/6)^2) + (59/36)).dx`

I = `1/sqrt3 int 1/sqrt((x + 5/6)^2 + (sqrt59/6)^2)dx`

I = `1/sqrt3 log |(x + 5/6) +sqrt((x + 5/2)^2 + (sqrt59/6)^2)| + c`   ....`int1/sqrt(x^2 + a^2)dx = log|x + sqrt(x^2 + a^2)| + c`

I = `1/sqrt3 . log|(x + 5/6) + sqrt(x^2 + (5x)/3 + 7/3)| + c` 

  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Exercise 3.2 (B) [Page 123]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Exercise 3.2 (B) | Q 1.14 | Page 123

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