72 lines
2.1 KiB
TeX
72 lines
2.1 KiB
TeX
\section{Integral Tables}
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\label{app:integral_tables}
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This appendix provides commonly used integral formulas encountered throughout the handbook.
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\subsection{Basic Integrals}
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\label{sec:appC_basic}
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\begin{table}[htbp]
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\centering
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\caption{Basic Integral Formulas}
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\label{tab:integrals_basic}
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\begin{tabular}{l l}
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\toprule
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\textbf{Integrand} & \textbf{Result} \\
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\midrule
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$\displaystyle \int x^n \, dx$ & TBD \\
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$\displaystyle \int \frac{1}{x} \, dx$ & TBD \\
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$\displaystyle \int e^{ax} \, dx$ & TBD \\
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$\displaystyle \int a^x \, dx$ & TBD \\
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$\displaystyle \int \sin(ax) \, dx$ & TBD \\
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$\displaystyle \int \cos(ax) \, dx$ & TBD \\
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$\displaystyle \int \tan(ax) \, dx$ & TBD \\
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$\displaystyle \int \sec^2(ax) \, dx$ & TBD \\
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$\displaystyle \int \csc^2(ax) \, dx$ & TBD \\
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$\displaystyle \int \sec(ax)\tan(ax) \, dx$ & TBD \\
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$\displaystyle \int \csc(ax)\cot(ax) \, dx$ & TBD \\
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\bottomrule
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\end{tabular}
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\end{table}
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\subsection{Integrals Involving Exponential and Trigonometric Functions}
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\label{sec:appC_exptig}
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\begin{table}[htbp]
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\centering
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\caption{Exponential--Trigonometric Integrals}
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\label{tab:integrals_exptig}
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\begin{tabular}{l l}
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\toprule
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\textbf{Integrand} & \textbf{Result} \\
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\midrule
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$\displaystyle \int e^{ax}\sin(bx)\,dx$ & TBD \\
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$\displaystyle \int e^{ax}\cos(bx)\,dx$ & TBD \\
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$\displaystyle \int x e^{ax}\,dx$ & TBD \\
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$\displaystyle \int x \sin(ax)\,dx$ & TBD \\
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$\displaystyle \int x \cos(ax)\,dx$ & TBD \\
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$\displaystyle \int \ln(x)\,dx$ & TBD \\
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\bottomrule
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\end{tabular}
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\end{table}
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\subsection{Integrals Involving Inverse Trigonometric Functions}
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\label{sec:appC_inverse_trig}
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\begin{table}[htbp]
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\centering
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\caption{Inverse Trigonometric Integrals}
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\label{tab:integrals_inverse_trig}
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\begin{tabular}{l l}
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\toprule
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\textbf{Integrand} & \textbf{Result} \\
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\midrule
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$\displaystyle \int \frac{1}{\sqrt{a^2 - x^2}}\,dx$ & TBD \\
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$\displaystyle \int \frac{1}{a^2 + x^2}\,dx$ & TBD \\
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$\displaystyle \int \frac{1}{x\sqrt{x^2 - a^2}}\,dx$ & TBD \\
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$\displaystyle \int \sqrt{a^2 - x^2}\,dx$ & TBD \\
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$\displaystyle \int \frac{1}{\sqrt{x^2 + a^2}}\,dx$ & TBD \\
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\bottomrule
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\end{tabular}
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\end{table}
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