\( \int _ { 1 } ^ { 5 } \frac { 1 } { x } dx , F ( x ) = \ln ( x ) \)

Did you know that the integral of \( \frac{1}{x} \) is one of the most celebrated integrals in calculus? It brings us to the natural logarithm function! So, when you evaluate \( \int_{1}^{5} \frac{1}{x} dx \), you're essentially calculating the difference between the natural logs at the bounds, which is \( \ln(5) - \ln(1) = \ln(5) \), since \( \ln(1) = 0 \). Now, why is this important in real life? The natural logarithm frequently appears in fields like finance, biology, and physics. For instance, it’s used in calculating compound interest and population growth models. So, while it may seem like just a math problem, it's a concept that builds the foundations for many real-world applications!