Formulas, etc

Question 1

Answer 1

Question 2

Answer 2

Question 3

Answer 3

Question 4

Answer 4

Question 5

Answer 5

Question 6

Answer 6

Question 7

Answer 7

Question 8

Answer 8

Question 9

Integration by Parts

Answer 9

Question 10

Integration by Parts - Steps

Answer 10

Question 11

Answer 11

Question 12

Answer 12

Question 13

Answer 13

Question 14

Answer 14

Question 15

Answer 15

Question 16

Answer 16

Question 17

Answer 17

Question 18

Answer 18

Question 19

Answer 19

Question 20

Answer 20

Question 21

Answer 21

Question 22

Answer 22

Question 23

Answer 23

Question 24

Answer 24

Question 25

Answer 25

Question 26

To perform a PFD

Answer 26

Degree of the Numerator < Degree of the Denominator.

If it is not, one must perform long division first.

Q(x) must be factored completely:

only linear and/or irreducible quadratic factors.

Question 27

Case I: Q(x) is the product of distinct linear factors.

Answer 27

Question 28

Case II: Q(x) is the product of linear factors where some are repeated.

Answer 28

Question 29

Case III: Q(x) contains irreducible quadratic factors that are not repeated.

Answer 29

Question 30

Case IV: Q(x) contains a repeated irreducible quadratic factors.

Answer 30

Question 31

Determine the coefficients - Method 1: Substitute in (1) values of x. Start with the roots of Q(x)

Answer 31

Question 32

Determine the coefficients:

Method 2: Expand the right hand side of (1), collect like terms and match the coefficients of the powers of x.

Answer 32