#### Calculus Early Transcendentals / Ch. 7

Integration by parts rule

∫udv= uv-∫vdu

tabular integration

short cut * shortcut only works on polynomials x exponentials with sin or cos

Trig Integrals

∫cotxdx = ln|sinx|+C∫tanxdx = ln|secx|+C∫secxdx= ln|tanx+secx|+C∫cscxdx= ln|cscx-cotx|+C

Pythagorean Identities

sin^2x+cos^2x=11+tan^2x=sec^2x1+cot^2x=csc^2x

Sum and Difference Formulas (***MEMORIZE!!!)

sin[x(+/-)y]=sin(x)cos(y)[+/-]cos(x)sin(y)cos[x(+/-)y]=cos(x)cos(y)[-/+]sin(x)sin(y)----notice that for cos, if it is positive in the first part, is negative in the second part tan[x(+/-)y]=tan(x)[+/-]tan(y)/1[-/+]tan(x)tan(y)---notice that the top and bottom are opposite of each other

Double Angle Formulas

sin(2x)=2sin(x)cos(x)cos(2x)=cos^2-sin^2=1-2sin^2=2cos^2-1tan(2x)=2tanx/1-tan^2

Power-Reducing Formulas

sin^2 x = (1 - cos 2x)/(2) cos^2 x = (1 + cos 2x)/(2)

Half Angle Formulas

sin x/2 = + or - √(1 - cos x)/2cos x/2 = + or - √1 + cos x)/2tan x/2 = (1 - cos x)/(sin x) or (sin x)/(1 + cos x)

Partial Fractions

one of the fractions that was added or subtracted to result in a given rational expression

Simpson's Method

2 mid + trap/ 3