diff --git a/codes/Math/Equations.tex b/codes/Math/Equations.tex index d08f910f..33eb060b 100644 --- a/codes/Math/Equations.tex +++ b/codes/Math/Equations.tex @@ -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 - \( - \begin{aligned} + \begin{tabular}{|*{20}{>{$\displaystyle}c<{$}|}} \frac{d}{dx}\sin^{-1} x = \frac{1}{\sqrt{1-x^2}} & \frac{d}{dx}\cos^{-1} x = -\frac{1}{\sqrt{1-x^2}} @@ -52,12 +51,12 @@ \subsubsection{Derivatives/Integrals} \\ \int e^{-x^2} = \frac{\sqrt \pi}{2} \text{erf}(x) & - \int xe^{ax}dx = \frac{e^{ax}}{a^2}(ax-1) + \int xe^{ax} dx = \frac{e^{ax}}{a^2}(ax-1) \\ - \end{aligned} - \) + \end{tabular} \( + \displaystyle \int \sqrt{a^2 + x^2} = \frac{1}{2} \left(x\sqrt{a^2+x^2} + a^2 \operatorname{asinh}(x/a) \right) \) }