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author | Thomas Albers <thomas@thomaslabs.org> | 2023-03-08 23:43:00 +0100 |
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committer | Thomas Albers <thomas@thomaslabs.org> | 2023-03-08 23:43:00 +0100 |
commit | 61b5ce20f25c5785e41574998a12c6d06eb05a5e (patch) | |
tree | 20e2225b4f30b15d8dee30351041d1f33d42b34a /src/math/integrals.org | |
parent | 561bac75579391c14e47eaccfabdf9eda98855da (diff) |
Diffstat (limited to 'src/math/integrals.org')
-rw-r--r-- | src/math/integrals.org | 35 |
1 files changed, 35 insertions, 0 deletions
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*} |