Question

Integrate the following functions with respect to x:

`sqrt((x + 1)^2 - 4)`

Answer 1

`int sqrt((x + 1)^2 - 4)  "d"x = int sqrt((x + 1)^2 - 2^2)  "d"x`

Put x + 1 = t

dx = dt

= `int sqrt("t"^2 - 2^2)  "dt"`

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

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

`int sqrt((x + 1)^2 - 4)  "d"x = ((x + 1))/2 sqrt((x + 1)^2 - 4) - 2 log |(x + 1) + sqrt((x + 1)^2 - 4)| + "c"`