Evaluate ∫ 1 / 1 + x dx

To evaluate the integral ∫ 1 / (1 + x) dx, we can use a simple substitution method. This integral is a standard form that leads to the natural logarithm.

Step-by-Step Solution

1. **Identify the integral**: We have the integral of the function 1 / (1 + x).

2. **Use the formula**: The integral of 1 / (a + x) is given by ln|a + x| + C, where C is the constant of integration.

3. **Apply the formula**: In our case, a = 1. Therefore, we can write:

∫ 1 / (1 + x) dx = ln|1 + x| + C

Final Result

The evaluated integral is:

ln|1 + x| + C

This result shows how the function behaves as x changes, and the constant C represents any constant value that could be added to the integral.