skeleton: 14 chapter stubs and 4 appendices

appendices/appC_integral_tables.tex

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+\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}