Question

Integrate the following with respect to x.

`1/(2x^2 - 9)`

Answer 1

`int 1/(2x^2 - 9)  "d"x = int 1/((sqrt(2x))^2 - 3^2)  "d"x`

Let t = `sqrt(2)x`

Then dt = `sqrt(2)  "dt"`

= `1/2 int "dt"/("t"^2 - 3^2)`

= `1/sqrt(2) 1/(2(3)) log |("t" - 3)/("t" + 3)| + "c"`

= `1/(6sqrt(2)) log |(sqrt(2x) - 3)/(sqrt(2x) + 3)| + "c"`