\section{Integral Tables}
\label{app:integral_tables}

This appendix provides commonly used integral formulas encountered throughout the handbook.

\subsection{Basic Integrals}
\label{sec:appC_basic}

\begin{table}[htbp]
\centering
\caption{Basic Integral Formulas}
\label{tab:integrals_basic}
\begin{tabular}{l l}
\toprule
\textbf{Integrand} & \textbf{Result} \\
\midrule
$\displaystyle \int x^n \, dx$ & TBD \\
$\displaystyle \int \frac{1}{x} \, dx$ & TBD \\
$\displaystyle \int e^{ax} \, dx$ & TBD \\
$\displaystyle \int a^x \, dx$ & TBD \\
$\displaystyle \int \sin(ax) \, dx$ & TBD \\
$\displaystyle \int \cos(ax) \, dx$ & TBD \\
$\displaystyle \int \tan(ax) \, dx$ & TBD \\
$\displaystyle \int \sec^2(ax) \, dx$ & TBD \\
$\displaystyle \int \csc^2(ax) \, dx$ & TBD \\
$\displaystyle \int \sec(ax)\tan(ax) \, dx$ & TBD \\
$\displaystyle \int \csc(ax)\cot(ax) \, dx$ & TBD \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Integrals Involving Exponential and Trigonometric Functions}
\label{sec:appC_exptig}

\begin{table}[htbp]
\centering
\caption{Exponential--Trigonometric Integrals}
\label{tab:integrals_exptig}
\begin{tabular}{l l}
\toprule
\textbf{Integrand} & \textbf{Result} \\
\midrule
$\displaystyle \int e^{ax}\sin(bx)\,dx$ & TBD \\
$\displaystyle \int e^{ax}\cos(bx)\,dx$ & TBD \\
$\displaystyle \int x e^{ax}\,dx$ & TBD \\
$\displaystyle \int x \sin(ax)\,dx$ & TBD \\
$\displaystyle \int x \cos(ax)\,dx$ & TBD \\
$\displaystyle \int \ln(x)\,dx$ & TBD \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Integrals Involving Inverse Trigonometric Functions}
\label{sec:appC_inverse_trig}

\begin{table}[htbp]
\centering
\caption{Inverse Trigonometric Integrals}
\label{tab:integrals_inverse_trig}
\begin{tabular}{l l}
\toprule
\textbf{Integrand} & \textbf{Result} \\
\midrule
$\displaystyle \int \frac{1}{\sqrt{a^2 - x^2}}\,dx$ & TBD \\
$\displaystyle \int \frac{1}{a^2 + x^2}\,dx$ & TBD \\
$\displaystyle \int \frac{1}{x\sqrt{x^2 - a^2}}\,dx$ & TBD \\
$\displaystyle \int \sqrt{a^2 - x^2}\,dx$ & TBD \\
$\displaystyle \int \frac{1}{\sqrt{x^2 + a^2}}\,dx$ & TBD \\
\bottomrule
\end{tabular}
\end{table}