Calculus - Unit 6 Integrals

Basic Ones / Algebraic Methods

100

int_(0)^(pi)sin(x)dx

2

200

int_(2)^(\infty)\frac{1}{x^3}dx

1

300

int(x^2-4)/(3x)dx

x^2/6-4/3ln|x|+C

U-Substitution

100

inte^(5x)dx

1/5e^(5x)+C

200

intsin(ln(x))/(x)dx

-cos(ln(x))+C

300

intsin^2(3x)\cdotcos(3x)dx

1/9sin^3(3x)+C

By Parts

100

intx\cdote^xdx

xe^x-e^x+C

200

D

300

intx\cdotcos(2x)dx

1/2x\cdot sin(2x)+1/4cos(2x)+C

Partial Fractions

100

int(1)/((x+4)(x+1))dx

1/3ln|x+1|-1/3ln|x+4|+C

200

\int\frac{3x+1}{x^2-x-6}dx

2ln(x-3)+ln(x+2)+C

300

int(2)/(x-x^2)dx

2ln|x|-2ln|1-x|+C

You Decide

100

int1/(x^2+1)dx

arctan(x)+C

200

int(1)/(x^2-1)dx

1/2ln|x-1|-1/2ln|x+1|+C

300

intx/(x^2+1)dx

1/2ln(x^2+1)+C

Wild Card

100

The bowler and the fez are both types of these.

hats

200

THERE ARE ALLIGATORS IN THIS 1.5 MILLION- SQUARE-MILE NATIONAL PARK AUTHORIZED IN 1934

 EVERGLADES NATIONAL PARK

300

THIS ACADEMIC NO-NO COMES FROM A LATIN WORD MEANING "KIDNAPPING"

PLAGIARISM