2$\int x^pdx$
$\frac{1}{n+1}x^{n+1}+C$
3$\int cos(ax)dx$
$\frac{1}{a}sin(ax)+C$
4$\int sin(ax)dx$
$-\frac{1}{a}cos(ax)+C$
5$\int sec^2(ax)dx$
$\frac{1}{a}tan(ax)+C$
6$\int csc^2(ax)dx$
$-\frac{1}{a}cot(ax)+C$
7$\int sec(ax)tan(ax)dx$
$\frac{1}{a}sec(ax)+C$
8$\int csc(ax)cot(ax)dx$
$-\frac{1}{a}csc(ax)+C$
9$\int e^{ax}dx$
$\frac{1}{a}e^{ax}+C$
10$\int \frac{1}{x}dx$
$\ln|x|+C$
11$\int \frac{1}{a^2+x^2}dx$
$\frac{1}{a}\arctan(\frac{x}{a})+C$
12$\int \frac{1}{\sqrt{a^2+x^2}}dx$
$\arcsin(\frac{x}{a})+C$
13$\int \frac{1}{x\sqrt{a^2+x^2}}dx$
$\frac{1}{a}arcsec|\frac{x}{a}|+C$
14$\int\tan(ax)dx$
$\frac{1}{a}\ln|\sec(ax)|+C$
15$\int\cot(ax)dx$
$\frac{1}{a}\ln|\sin(ax)|+C$
16$\int\sec(ax)dx$
$\frac{1}{a}\ln|\sec(ax)+\tan(ax)|+C$
17$\int\csc(ax)dx$
$-\frac{1}{a}\ln|\csc(ax)+\cot(ax)|+C$
18What are the basic integration approaches?
u-substitution, split the fraction, long division, different of squares, completing the square
19What is the formula for integrating products?
$\int u dv = uv -\int vdu$ or $\int uv' = uv -\int vu'$
20How does tabular integration work?
Differentiate one of the multipliers until you reach zero, integrate the other multiplier. Multiply diagonally switching signs, and sum the results to get the answer.
21How do you pick u in product integrations?
1. Logarithms
2. Inverses
3. Algebraic (+,-,$\times$,$\div$,$\sqrt()$,$^n$)
4. Trig
5. Exponential
22$\int cos^2 xdx$
$\int \frac{1+cos(2x)}{2} dx$
23$\int sin^2 xdx$
$\int \frac{1-cos(2x)}{2} dx$
24What's the derivative of sin(x)?
$cos(x)$
25What's the derivitave of cos(x)?
$-sin(x)$
26What's the derivative of tan(x)?
$sec^2 x$
27What's the derivative of cot(x)?
$-csc^2 (x)$
28What's the derivative of sec(x)?
$sec(x)tan(x)$
29What's the derivative of csc(x)?
$-csc(x)cot(x)$
30List the pythagorean identities.
$sin^2 \theta+cos^2\theta=1$
$tan^2 \theta+1=sec^2\theta$
$1+cot^2 \theta=csc^2\theta$
31List the Product-To-Sum Identities
$\int sin(a)sin(b)=\frac{1}{2}\int cos(a-b)-cos(a+b)$
$\int cos(a)cos(b)=\frac{1}{2}\int cos(a-b)+cos(a+b)$
$\int sin(a)cos(b)=\frac{1}{2}\int sin(a-b)+sin(a+b)$
32What is the trig subsitution for $\sqrt{a^2-x^2}$ and what does it simplify to?
$x=a\sin{\theta}$ simplifies to $a\cos{\theta}$
33What is the trig subsitution for $\sqrt{x^2-a^2}$ and what does it simplify to?
$x=a\sec{\theta}$ simplifies to $a\tan{\theta}$
34What is the trig subsitution for $\sqrt{a^2+x^2}$ and what does it simplify to?
$x=a\tan{\theta}$ simplifies to $a\sec{\theta}$
35$\int \frac{1}{a^2+x^2}dx=$
$\frac{1}{a}\arctan{(\frac{x}{a})}+C$
36Algebraically describe Partial Fraction Decomposition
$\frac{A}{linear}+\frac{B}{linear}+\frac{C}{quadratic}$
37List the 4 cases of Partial Fraction Decomposition.
1. Multiple Linear Terms
2. Repeated Linear Terms
3. Quadratic Terms
4. Long Division $(Degree_{Top} \ge Degree_{Bottom})$