EXAM 1

Question 1

S a dx

Answer 1

ax + C

Question 2

S x^n dx

Answer 2

x^n+1 / n+1

Question 3

S (1/x) dx

Answer 3

ln |x| + c

Question 4

S e^x dx

Answer 4

s^x + c

Question 5

S a^x dx

Answer 5

a^x / ln(a) + c

Question 6

S ln(x) dx

Answer 6

xln(x) - x + c

Question 7

S cos(x) dx

Answer 7

sin(x) + c

Question 8

S sin(x) dx

Answer 8

-cos(x) + c

Question 9

S sec^2(x) dx

Answer 9

tan(x) + c

Question 10

(ln(x))’

Answer 10

1/x

Question 11

(e^x)’

Answer 11

e^x

Question 12

a^x =

Answer 12

e^(x*ln(a))

Question 13

logb(x) =

Answer 13

ln(x) / ln(b)

Question 14

(arcsinx)’

Answer 14

1 / sqrt(1-x^2)

Question 15

(arccosx)’

Answer 15

-1 / sqrt(1-x^2)

Question 16

(arctanx)’

Answer 16

1 / 1 + x^2

Question 17

(arcsec)’

Answer 17

1 / |x| sqrt(x^2-1)

Question 18

(arccsc)’

Answer 18

-1 / |x| sqrt(x^2-1)

Question 19

(arccot)’

Answer 19

-1 / 1+x^2

Question 20

Integration by parts formula

Answer 20

S u dv = uv-Svdu

Question 21

Functions hardest to easiest

Answer 21

LIATE (log, inverse, algebraic, trig, exponential)

Question 22

S csc^2 dx

Answer 22

-cot(x) + c

Question 23

S sec(x)tan(x) dx

Answer 23

sec(x) + c

Question 24

S csc(x)cot(x) dx

Answer 24

-csc(x) + x

Question 25

S tan(x) dx

Answer 25

ln |sec(x)| + c

Question 26

S cot(x) dx

Answer 26

ln |sin(x)| +c

Question 27

S sec(x) dx

Answer 27

ln |sec(x)+tan(x)| + c

Question 28

S csc(x) dx

Answer 28

ln |csc(x) - cot(x)| + c

Question 29

S sin^2(x) dx

Answer 29

S 1-cos(2x) / 2 dx

Question 30

S cos^2(x) dx

Answer 30

S 1+cos(2x) / 2

Question 31

1 - sin^2 u =

Answer 31

cos^2(u)

Question 32

1 + tan^2 u =

Answer 32

sec^2(u)

Question 33

sec^2 u - 1 =

Answer 33

tan^2(u)

Question 34

sqrt(a^2-x^2) , x =

Answer 34

asin(u)

Question 35

sqrt(a^2 + x^2), x =

Answer 35

atan(u)

Question 36

sqrt(x^2-a^2), x =

Answer 36

asec(u)