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Update derivatives table style
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OmeletWithoutEgg committed Feb 12, 2024
1 parent e5d0415 commit 2c867db
Showing 1 changed file with 6 additions and 7 deletions.
13 changes: 6 additions & 7 deletions codes/Math/Equations.tex
Original file line number Diff line number Diff line change
Expand Up @@ -31,12 +31,11 @@ \subsubsection{Derivatives/Integrals}
Integration by parts:
\(\int_a^bf(x)g(x)dx = [F(x)g(x)]_a^b-\int_a^bF(x)g'(x)dx\)
{
% \setlength{\tabcolsep}{1pt}
% \setlength{\columnsep}{0pt}
\setlength{\tabcolsep}{1pt}
\setlength{\columnsep}{0pt}

\noindent
\(
\begin{aligned}
\begin{tabular}{|*{20}{>{$\displaystyle}c<{$}|}}
\frac{d}{dx}\sin^{-1} x = \frac{1}{\sqrt{1-x^2}}
&
\frac{d}{dx}\cos^{-1} x = -\frac{1}{\sqrt{1-x^2}}
Expand All @@ -52,12 +51,12 @@ \subsubsection{Derivatives/Integrals}
\\
\int e^{-x^2} = \frac{\sqrt \pi}{2} \text{erf}(x)
&
\int xe^{ax}dx = \frac{e^{ax}}{a^2}(ax-1)
\int xe^{ax} dx = \frac{e^{ax}}{a^2}(ax-1)
\\
\end{aligned}
\)
\end{tabular}
\(
\displaystyle
\int \sqrt{a^2 + x^2} = \frac{1}{2} \left(x\sqrt{a^2+x^2} + a^2 \operatorname{asinh}(x/a) \right)
\)
}
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