Question

Evaluate : `∫dx/(4 - 9x^2)`

Answer 1

Let I = `∫dx/(4 - 9x^2)`

= `dx/(9(4/9 - x^2))`

= `1/9∫1/((2/3)^2 - x^2)`dx

= `1/9 . 1/(2 . 2/3) log|(2/3 + x)/(2/3 - x)| + "C"`               `(∵ ∫1/(a^2 - x^2) dx = 1/(2a) log|(a+x)/(a-x)|) + "C")`

⇒ I = `1/12 log|(2 + 3x)/(2 - 3x)| + "C"`