Question

How do you integrate `int (4x)/sqrt(x^2-49)dx` using trigonometric substitution?

Answer 1

`I = 4(x^2 - 49)^(1/2) +C`

Explanation:

Trig substitution can be used, but is not needed to solve this problem. If we let `u = x^2 - 49`, we see that `du = 2xdx` and `dx = (du)/(2x)`.

`I = int (4x)/sqrt(u) * du/(2x)`

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

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

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

`I = 4(x^2 - 49)^(1/2) +C`

Hopefully this helps!