Question

Integrate the following with respect to x.

`(6x + 7)/sqrt(3x^2 + 7x - 1)`

Answer 1

Let f(x) = 3x² + 7x – 1

Then f'(x) = 6x + 7

So `int (6x + 7)/sqrt(3x^2 + 7x - 1)  "d"x = int ("f'"(x))/("f"(x))  "d"x`

= `2sqrt("f"(x) + "c")`

= `2sqrt(3x^2 + 7x - 1 + "c")`