From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 9 Apr 2019 06:08:09 +0000 (+1000)
Subject: [spec] add to integral laws
X-Git-Tag: yr12~169
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/b99782992dd6859bf7e977aa5d4ba334806c51b0?ds=sidebyside

[spec] add to integral laws
---

diff --git a/spec/calculus.md b/spec/calculus.md
index a085f3b..5be3218 100644
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -1,3 +1,12 @@
+---
+geometry: margin=2cm
+columns: 2
+graphics: yes
+tables: yes
+author: Andrew Lorimer
+classoption: twocolumn
+---
+
 # Differential calculus
 
 ## Limits
@@ -228,8 +237,10 @@ $\int k f(x) dx = k \int f(x) dx$
 | $f(x)$                          | $\int f(x) \cdot dx$         |
 | ------------------------------- | ---------------------------- |
 | $k$ (constant) | $kx + c$ |
-| $x^n$ | ${1 \over {n+1}}x^{n+1} + c$ |
+| $x^n$ | ${x^{n+1} \over {n+1}} + c$ |
 | $a x^{-n}$ | $a \cdot \log_e x + c$ |
+| ${1 \over {ax+b}}$ | ${1 \over a} \log_e (ax+b) + c$ |
+| $(ax+b)^n$ | ${1 \over {a(n+1)}}(ax+b)^{n-1} + c$ |
 | $e^{kx}$ | ${1 \over k} e^{kx} + c$ |
 | $e^k$ | $e^kx + c$ |
 | $\sin kx$ | $-{1 \over k} \cos (kx) + c$ |
@@ -237,8 +248,6 @@ $\int k f(x) dx = k \int f(x) dx$
 | ${f^\prime (x)} \over {f(x)}$ | $\log_e f(x) + c$ |
 | $g^\prime(x)\cdot f^\prime(g(x)$ | $f(g(x))$ (chain rule)|
 | $f(x) \cdot g(x)$ | $\int [f^\prime(x) \cdot g(x)] dx + \int [g^\prime(x) f(x)] dx$ |
-| ${1 \over {ax+b}}$ | ${1 \over a} \log_e (ax+b) + c$ |
-| $(ax+b)^n$ | ${1 \over {a(n+1)}}(ax+b)^{n-1} + c$ |
 
 ## Applications of antidifferentiation