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 $\int u(x)v'(x) \, dx=uv-\int u'(x)v(x) \, dx$