Derivative of an accumulation function via FTC Part 1

By FTC Part 1, since $\ln(t)$ is continuous on the relevant interval, the accumulation function $F(x) = \int_1^x \ln(t)\, dt$ satisfies $F'(x) = \ln(x)$. This means differentiating $F$ simply recovers the integrand evaluated at $x$, with no need to find an antiderivative first.

Substituting $x = 4$ gives $F'(4) = \ln(4)$. This is the exact answer, which can also be written approximately as $\ln(4) \approx 1.386$.