1. The problem is to evaluate the definite integral $$\int_1^e \frac{1}{x} \, dx$$. 2. The formula for the integral of $$\frac{1}{x}$$ is $$\int \frac{1}{x} \, dx = \ln|x| + C$$, where $$\ln$$ is the natural logarithm. 3. Since this is a definite integral from 1 to $$e$$, we apply the Fundamental Theorem of Calculus: $$\int_1^e \frac{1}{x} \, dx = \left[ \ln|x| \right]_1^e = \ln|e| - \ln|1|$$. 4. Evaluate the logarithms: $$\ln e = 1$$ because $$e$$ is the base of the natural logarithm. $$\ln 1 = 0$$ because the logarithm of 1 is always zero. 5. Substitute these values back: $$1 - 0 = 1$$. 6. Therefore, the value of the integral is $$1$$.