From 61b5ce20f25c5785e41574998a12c6d06eb05a5e Mon Sep 17 00:00:00 2001
From: Thomas Albers <thomas@thomaslabs.org>
Date: Wed, 8 Mar 2023 23:43:00 +0100
Subject: Restructure build system and directory structures

---
 src/math/integrals.org | 35 +++++++++++++++++++++++++++++++++++
 1 file changed, 35 insertions(+)
 create mode 100644 src/math/integrals.org

(limited to 'src/math/integrals.org')

diff --git a/src/math/integrals.org b/src/math/integrals.org
new file mode 100644
index 0000000..a8e9677
--- /dev/null
+++ b/src/math/integrals.org
@@ -0,0 +1,35 @@
+#+title:Table of Integrals
+#+setupfile: ../../math_options.org
+
+* Disclaimer
+This site as of now just a technology demonstration and its claims
+should not be taken as true (even though I myself am pretty confident
+they are)
+
+* $a + bx$
+\begin{align*}
+\intg{(a + bx)^n}{\frac{(a+bx)^{n+1}}{b(n+1)}}\\
+\int\frac{\D{x}}{a + bx} &= \frac{1}{b}\log(a+bx) + C\\
+\int\frac{x\D{x}}{a + bx} &= \frac{1}{b^2}(a + bx - a\log(a+bx)) + C
+\end{align*}
+
+* Trigonometric Funtions
+\begin{align*}
+\intg{\sin(x)}{-\cos(x)}\\
+\intg{\cos(x)}{\sin(x)}\\
+\intg{\tan(x)}{-\ln(\cos(x))}\\
+\intg{\sec(x)}{\ln(\sec(x) + \tan(x))}\\
+\intg{\csc(x)}{-\ln(\csc(x) + \cot(x))}\\
+\intg{\cot(x)}{\ln(\sin(x))}
+\end{align*}
+* Hyperbolic Funtions as results
+\begin{align*}
+\int\frac{\text{d}x}{\sqrt{x^2 + a^2}} &= \arsinh{\frac{x}{a}} + C\\
+\int\frac{\text{d}x}{\sqrt{x^2 - a^2}} &= \arcosh{\frac{x}{a}} + C\\
+\int\frac{\text{d}x}{a^2 - x^2} &= \frac{1}{a}\artanh{\frac{x}{a}} + C\\
+%\int\frac{\text{d}x}{x^2 - a^2} &= -\frac{1}{a}\arcoth{\frac{x}{a}} + C\\
+\int\frac{\text{d}x}{x\sqrt{a^2 - x^2}} &= -\frac{1}{a}\arsech{\frac{x}{a}} + C\\
+\int\frac{\text{d}x}{x\sqrt{x^2 + a^2}} &= -\frac{1}{a}\arcsch{\frac{x}{a}} + C\\
+\intg{\sqrt{x^2+a^2}}{\frac{x}{2}\sqrt{x^2+a^2} + \frac{a^2}{2}\arsinh{\frac{x}{a}}}\\
+\intg{\sqrt{x^2-a^2}}{\frac{x}{2}\sqrt{x^2-a^2} - \frac{a^2}{2}\arcosh{\frac{x}{a}}}
+\end{align*}
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