Math Snap

STEP 1

1. The integral to solve is $\int_{0}^{1} \frac{1}{1+x} \, dx$.
2. This is a definite integral involving a natural logarithm function.

STEP 2

1. Identify the integral form.
2. Evaluate the integral.
3. Apply the limits of integration.
4. Simplify the result.

STEP 3

Recognize that the integral $\int \frac{1}{1+x} \, dx$ is the natural logarithm function:
$$\int \frac{1}{1+x} \, dx = \ln|1+x| + C$$

STEP 4

Evaluate the integral from 0 to 1:
$$\int_{0}^{1} \frac{1}{1+x} \, dx = \left[ \ln|1+x| \right]_{0}^{1}$$

STEP 5

Apply the limits of integration:
$$\left[ \ln|1+x| \right]_{0}^{1} = \ln|1+1| - \ln|1+0|$$ $$= \ln 2 - \ln 1$$

Simplify the result:
Since $\ln 1 = 0$, we have:
$$\ln 2 - 0 = \ln 2$$ The value of the integral is:
$$\boxed{\ln 2}$$ However, none of the provided options match $\ln 2$ directly. Please verify the problem statement or options.