MATH201/content/Things to remember.md

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