\section*{Aufgabe 4}

\begin{align*}
	I &= \int_0^1 \frac{1}{1+4x} dx\\
    &= \int_0^{0.5} \frac{1}{1+4x} dx +\int_{0.5}^{1} \frac{1}{1+4x} dx\\
    &= (0.5 - 0) \cdot \frac{f(0) + f(0.5)}{2} + (1 - 0.5) \cdot \frac{f(1) + f(0.5)}{2} \\
    &= \frac{7}{15}
\end{align*}