Question

How do you integrate `\int \frac { x + 1} { \sqrt { x ^ { 2} + 2x - 4} } d x`?

Answer 1

Let `u = x^2 + 2x - 4`. Then `du = 2x + 2dx`.

`I = (x + 1)/sqrt(u) * (du)/(2x + 2)`

`I = (x +1)/sqrt(u) * (du)/(2(x + 1))`

`I = 1/(2sqrt(u)) du`

`I = 1/2u^(-1/2) du`

`I = u^(1/2) + C`

`I = (x^2 + 2x - 4)^(1/2) + C`

Hopefully this helps!