Calculus II Test 2 7.1-7.5

Question 1

formula for integration by parts

Answer 1

integral of udv= uv- integral of vdu

Question 2

integral of ln(x)dx

Answer 2

x*ln(x)-x+C

Question 3

Trig substitution if the integral contains a^2-x^2

Answer 3

x=a*sin(theta)

Question 4

Trig substitution if the integral contains a^2+x^2

Answer 4

x=a*tan(theta)

Question 5

Trig substitution if the integral contains x^2-a^2

Answer 5

x=a*sec(theta)

Question 6

Partial fractions with simple linear factors procedure

Answer 6

1. factor the denominator
2. put in partial fraction decomp form
3. put over common denominator
4. solve for constant numerators

Question 7

Partial fractions with repeated linear factors

Answer 7

same procedure except for part 2:
if (x-r)^m is in the denominator put in partial fraction decomp form;
A/(x-r)+ B/(x-r)^2+ C/(x-r)^3+ D/(x-r)^m