Unit 6

Question 1

∫sin(x) dx

Answer 1

-cos(x) + C

Question 2

∫cos(x) dx

Answer 2

sin(x) + C

Question 3

∫sec^2 dx

Answer 3

tan(x) + C

Question 4

∫csc^2 dx

Answer 4

-cot(x) + C

Question 5

∫sec(x)tan(x) dx

Answer 5

sec(x) + C

Question 6

∫csc(x)cot(x) dx

Answer 6

-csc(x) + C

Question 7

∫(1/x) dx

Answer 7

ln|x| + C

Question 8

∫e^x dx

Answer 8

e^x + C

Question 9

∫b^x dx

Answer 9

(1/(lnb)) * b^x + C

Question 10

∫1/ ( √1 - x^2)dx

Answer 10

arcsinx + C if |x| < 1

Question 11

∫1/(1 + x^2) dx

Answer 11

arctanx + C

Question 12

∫1/ x( √x^2 -1)

Answer 12

arcsecx + C if |x| < 1

Question 13

used for a quotient of polynomials when the degree of the numerator is greater than or equal to the degree of the denominator

Answer 13

Long Division

Question 14

Used for a quotient of polynomials when the denominator can be factored into linear non repeating factors

Answer 14

Partial Fractions

Question 15

When the degree of the denominator is greater than the degree of the numerator

Answer 15

Partial Fractions

Question 16

Logarithmic

Answer 16

1

Question 17

Inverse Trig

Answer 17

2

Question 18

Algebraic

Answer 18

3

Question 19

Trig

Answer 19

4

Question 20

Exponential

Answer 20

5

Question 21

Two functions multiplied together (ex. xln(x))

Answer 21

By Parts

Question 22

Integration by Parts

Answer 22

∫udv = uv - ∫vdu