$U_A = f(U_E)$ mit III. $\qquad\qquad\qquad\qquad\qquad\quad$ $\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad\qquad$
 $U_A=\color{blue}{-U_D}-U_C$ mit II. und I. $\color{blue}{U_D} = { 1 \over A_D } \cdot U_A \overset{A_D \rightarrow \infty}\longrightarrow 0$ $\qquad\qquad\qquad\qquad\qquad\quad$ $\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad\qquad$
 $U_A= \quad 0 \quad -\color{blue}{U_C}$ mit V. $\color{blue}{U_C}={ 1 \over C }\cdot(\int_{t_0}^{t_1} I_C \ dt+ Q_0(t_0))$ $\qquad\qquad\qquad\qquad\qquad\quad$ $\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad\qquad$
 $U_A = {-{ 1 \over C }\cdot}(\int_{t_0}^{t_1} \color{blue}{I_C} \ dt+ Q_0(t_0))$ mit IV. $\color{blue}{I_C}=I_R$ $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$
 $U_A = \color{blue}{-{ 1 \over C }\cdot(}\int_{t_0}^{t_1} I_R \ dt+ Q_0(t_0)\color{blue}{)}$ Ausklammern $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$
 $U_A = -{ 1 \over C }\cdot\int_{t_0}^{t_1} I_R \ dt - \color{blue}{ Q_0(t_0) \over C }$ Integrationskonstante betrachten $\color{blue}{ Q_0(t_0) \over C }= U_C(t_0) = -U_{A0}$ $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$
 $U_A = -{ 1 \over C }\cdot\int_{t_0}^{t_1} \color{blue}{I_R} \ dt + U_{A0}$ mit VI. und II. $\color{blue}{I_R}={ U_R \over R}={ U_E \over R}$ $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$
 $U_A = -{ 1 \over C }\cdot\int_{t_0}^{t_1} \color{blue}{1 \over R} \cdot U_E \ dt + U_{A0}$ Konstante vorziehen $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$
 $U_A = -{ 1 \over {R\cdot C} }\cdot\int_{t_0}^{t_1} U_E \ dt + U_{A0}$ Zeitkonstante $\tau = R \cdot C$ einfügen $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$
 $U_A = -{ 1 \over {\tau} }\cdot\int_{t_0}^{t_1} U_E \ dt + U_{A0}$ $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad$ $\qquad\qquad\qquad\qquad\qquad\qquad\qquad$