Test 1

Question 1

Integration by Parts Formula

Answer 1

∫ udv = [uv - ∫( vdu )]

Question 2

d/dx C=

Answer 2

0

Question 3

d/dx x=

Answer 3

1

Question 4

d/dx (x^n)

Answer 4

n*x^(n-1)

Question 5

d/dx (Cx)=

Answer 5

C d/dx (x)

Question 6

d/dx (x*v)=

Answer 6

x * d/dx[v] + v* d/dx[x]

Question 7

d/dx (x/v)=

Answer 7

(( v * d/dx[x] - x * d/dx[v] )) / 2

Question 8

d/dx [(f*g)(x)]=
chain rule

Answer 8

f’(g(x)) * g’(x)

Question 9

d/dx e^x=

Answer 9

e^x

Question 10

d/dx (1/x)

Answer 10

-1/x^2

Question 11

d/dx a^x=

Answer 11

a^x * ln(a)

Question 12

d/dx ln |x|=

Answer 12

1/x

Question 13

d/dx loga |x|=

Answer 13

1 / (ln(a))x

Question 14

Lim as x-> ∞ of (f(x)/g(x))=
LH’opital’s Rule

Answer 14

f’(x)/ g’(x)

Question 15

∫x^n dx=

Answer 15

( x^(n+1) ) / (n+1)

Question 16

∫ 1/x^2 dx =

Answer 16

-1/x + C

Question 17

∫1/x dx=

Answer 17

ln (x) + c

Question 18

∫ 1/(x+3) =

Answer 18

ln (|x+3|) + C

Question 19

1

Answer 19

1

Question 20

d/dx [sinx] =

Answer 20

cos x

Question 21

∫ cos x dx=

Answer 21

sin x + C

Question 22

d/dx [cos x]=

Answer 22

• sin x

Question 23

∫-sin x dx=

Answer 23

cos x + C

Question 24

∫ sin x dx =

Answer 24

-cos x + C

Question 25

d/dx [tan x] =

Answer 25

sec^2 x

Question 26

∫ sec^2 x=

Answer 26

tan x + C

Question 27

d/dx [cot x] =

Answer 27

-csc^2 x

Question 28

∫ csc^2 (x) dx =

Answer 28

-cot x + C

Question 29

∫ -csc^2 (x) dx=

Answer 29

cot x + C

Question 30

d/dx sec x=

Answer 30

sec x tan x

Question 31

∫ sec x tan x dx=

Answer 31

sec x + C

Question 32

d/dx [csc x] =

Answer 32

-csc x cot x

Question 33

∫ [-csc x cot x ] dx =

Answer 33

csc x

Question 34

∫ [csc x cot x] dx =

Answer 34

-csc x

Question 35

∫ [a^x] dx =

Answer 35

(a^x) /ln a

Question 36

∫ sec^3 (x) dx =

Answer 36

1/2 (sec x tan x + ln(|sec x + tan x|) + C

Question 37

∫ tan x dx=

Answer 37

ln (| sec x |) + C

Question 38

∫ cot x dx =

Answer 38

ln (| sin x |) + C

Question 39

∫ tan x dx =

Answer 39

ln (| sec x |) + C

Question 40

∫ cot x dx =

Answer 40

ln (| sin x |) + C

Question 41

∫ sec x dx =

Answer 41

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

Question 42

∫ csc x dx =

Answer 42

• ln (| css x + cot x |) + C = (( ln (| csc x - cot x |) + C ))

Question 43

∫csc^3 (x) dx =

Answer 43

• 1/2 (csc x cot x + ln (|csc x + cot x|) + C

Question 44

Answer 44

Question 45

Answer 45

Question 46

Answer 46

Question 47

cos^2 (x )=

Answer 47

1/2 (1+cos (2x))

Question 48

sin^2 (x) =

Answer 48

1/2 (1 - cos(2x))