Question

How do you evaluate the definite integral `int (2)/(2x+5) * dx` from `[1, e]`?

Answer 1

Use substitution.

Explanation:

`int_1^e (2)/(2x+5) * dx = int_1^e 1/(2x+5) 2 dx`

Let `u = 2x+5` so `du = 2dx` and

when `x=1`, `u=7` and

when `x=e`, `u = 2e+5`

`int_1^e 1/(2x+5) 2 dx = int_7^(2e+5) 1/u du`

`= lnu]_7^(2e+5)`

`= ln(2e+5)-ln7`