Notes for Math 220, Calculus 2

\begin{align*} \int k \, dx =\\ \text{For } a \neq 1, \int x^a \, dx = \amp\hspace{5cm} \text{, but } \int \frac{1}{x}\, dx = \int x^{-1} \, dx =\\ \int e^x\, dx = \amp\hspace{5cm} \int a^x\, dx =\\ \int \sin x\, dx = \amp\hspace{5cm} \int \cos x\, dx =\\ \int \tan x\, dx = \amp\hspace{5cm} \int \sec x\, dx =\\ (\dagger) \int \cot x \, dx = \amp\hspace{5cm} (\dagger) \int \csc x\, dx =\\ \int \sec^2 x\, dx = \amp\hspace{5cm} \int \sec x \tan x\, dx =\\ (\dagger) \int \csc^2 x\, dx = \amp\hspace{5cm} (\dagger) \int \csc x \cot x\, dx =\\ \int \frac{1}{\sqrt{a^2-x^2}} dx =\\ \int \frac{1}{\sqrt{x^2 + a^2}} dx = \amp\hspace{5cm} \int \frac{1}{a^2+x^2}\ dx =\\ \int \frac{1}{\sqrt{x^2 - a^2}} dx = \amp\hspace{5cm} \int \frac{1}{x^2-a^2} dx =\\ \int \sinh x\, dx = \amp\hspace{5cm} \int \cosh x\, dx =\\ \int \tanh x\, dx = \amp\hspace{5cm} \int \sech\ x\, dx = \end{align*}