Question

How do you evaluate the definite integral `int 1/(x^2+6x+9)` from `[0,1]`?

How do you evaluate the definite integral `int 1/(x^2+6x+9)dx` from `[0,1]`?

Answer 1

`1/12`.

Explanation:

`int_0^1 1/(x^2+6x+9)dx=int_0^1 1/(x+3)^2dx`

`=[-1/(x+3)]_0^1`

`=-[1/4-1/3]`

`=1/12`.