Integration Rules
$\int x^n dx = \frac{x^{n+1}}{n+1} + C$
$\int e^x dx = e^x + C$
$\int \frac{1}{x} dx = \ln|x| + C$
$\int \sin(x) dx = -\cos(x) + C$
$\int \cos(x) dx = \sin(x) + C$
By Parts:
$\int u \, dv = uv - \int v \, du$
Series Tests
Ratio Test:
$L = \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right|$
If $L < 1$ converges, $L > 1$ diverges.
p-Series:
$\sum \frac{1}{n^p}$ converges if $p > 1$.
Taylor Series
$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}$
$\sin(x) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{(2n+1)!}$
$\cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!}$
