Evaluate: `int(x+1)/(x^2+4x+5)\ dx`

Explanation

To evaluate the integral \( I = \int \frac{x+1}{x^2 + 4x + 5} \, dx \), we will use the method of integration by parts and partial fractions.

### Step 1: Rewrite the integrand
We start by rewriting the integrand. We can express the numerator \( x + 1 \) in terms of the derivative of the denominator \( x^2 + 4x + 5 \).

The derivative of the denominator is:
\[
\frac{d}{dx}(x^2 + 4x + 5) = 2x + 4.
...