25 lines
757 B
Markdown
25 lines
757 B
Markdown
This is an incomplete list. I'm trying to add to it as I go.
|
|
|
|
everything with the #remember tag as well as the representations of the various DE, they start with #de_
|
|
|
|
Also remember the following:
|
|
## derivatives of trigs
|
|
$\frac{d}{dx}\tan(x)=sec^2(x)$
|
|
$\frac{d}{dx}sec(x)=sec(x)\tan(x)$
|
|
$\frac{d}{dx}\csc=-\csc x\cot x$
|
|
$\frac{d}{dx}\cot (x)=-\csc^2(x)$
|
|
## integrals of trigs
|
|
$\int \tan(x) \, dx=\ln\mid \sec(x)\mid+C$
|
|
$\int sec(x) \, dx=\ln\mid sec(x)+\tan(x)\mid+C$
|
|
$\int \csc x \, dx=-\ln|\csc x+\cot x|+C$
|
|
$\int \cot x \, dx=-\ln|\csc x|+C$
|
|
|
|
## Integrals:
|
|
$\int \frac{1}{1+x^2} \, dx=\arctan(x)+C$
|
|
|
|
|
|
## integration by parts
|
|
LIATE -> log, inv trig, algebraic, trig, exp
|
|
set u to the first in the list above
|
|
$\int u(x)v'(x) \, dx=uv-\int u'(x)v(x) \, dx$
|