Question

Integrate the following with respect to x.

`1/sqrt(x^2 - 3x + 2)`

Answer 1

`int ("d"x)/sqrt(x^2 - 3x + 2) = int ("d"x)/sqrt((x - 3/2)^2 - 9/4 + 2)``

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

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

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