Differentiation/Integration

Question 1

Reciprocal Identity

1

cos

Answer 1

sec

Question 2

Pythagorean Identity

1+cot^2=

Answer 2

csc^2

Question 3

cosacosb+sinasinb

Answer 3

cos(a-b)

Question 4

Pythagorean Identity

sec^2

Answer 4

1+tan^2=sec^2

Question 5

∫ cscxcotx dx

Answer 5

-cscx + C

Question 6

∫secx dx

Answer 6

ln Isecx + tanxI + C

Question 7

Pythagorean Identity

sin and cos

Answer 7

sin^2+cos^2=1

Question 8

∫ x^n dx

Answer 8

x^(n+1) / n+1 (n cannot =-1)

Question 9

sinacosb+cosasinb

Answer 9

sin(a+b)

Question 10

∫ e^x dx

Answer 10

e^x + C

Question 11

d/dx (lnx)

Answer 11

1/x

Question 12

Pythagorean Identity

cot and csc

Answer 12

1+cot^2=csc^2

Question 13

Pythagorean Identity

csc^2

Answer 13

1+cot^2=csc^2

Question 14

d/dx (cotx)

Answer 14

-csc²x

Question 15

∫ 1/x dx

Answer 15

ln |x| + C

Question 16

cos(a+b)

Answer 16

cosacosb-sinasinb

Question 17

∫ sec²x dx

Answer 17

tanx + C

Question 18

sinacosb-cosasinb

Answer 18

sin(a-b)

Question 19

∫ secxtanx dx

Answer 19

secx + C

Question 20

d/dx (cscx)

Answer 20

-cscxcotx

Question 21

d/dx (x^n)

Answer 21

nx^n-1

Question 22

Pythagorean Identity

tan and secant

Answer 22

1+tan^2=sec^2

Question 23

∫ 1 dx

xlnx

Answer 23

ln I lnx I + C

Question 24

n

Σi²

ⁱ⁼¹

Answer 24

n(n+1)(2n+1)

6

Question 25

Pythagorean Identity

sin^2+cos^2=

Answer 25

1

Question 26

d/dx (sinx)

Answer 26

cosx

Question 27

sin(a+b)

Answer 27

sinacosb+cosasinb

Question 28

d/dx (secx)

Answer 28

secxtanx

Question 29

Reciprocal Identities

Cot

Answer 29

1

tan

Question 30

n

Σi

i=1

Answer 30

n(n+1)

2

Question 31

∫ xsinx dx

Answer 31

sinx - xcosx + C

Question 32

∫ xe^x dx

Answer 32

(x-1)e^x + C

Question 33

n

Σi³

i=1

Answer 33

n²(n+1)²

⁴

Question 34

d/dx (x)

Answer 34

1

Question 35

∫ a dx

Answer 35

ax + C

Question 36

n

Σc

i=1

Answer 36

cn

Question 37

∫ tanx dx

Answer 37

-ln Icos xI + C

Question 38

∫cot²x dx

Answer 38

-cotx - x + C

Question 39

d/dx (ax)

Answer 39

a

Question 40

Reciprocal Identity

csc

Answer 40

1

sin

Question 41

d/dx (cosx)

Answer 41

-sinx

Question 42

∫ 1 dx

Answer 42

x + C

Question 43

∫ a^x dx

Answer 43

a^x / lna +c (a>0, a cannot =1)

Question 44

∫ln x dx

Answer 44

x ln x - x + C

Question 45

∫ xcosx dx

Answer 45

cosx + xsinx + C

Question 46

∫ csc²x dx

Answer 46

-cotx + C

Question 47

∫ sinx dx

Answer 47

-cosx + C

Question 48

∫ cosx dx

Answer 48

sinx + C

Question 49

tan identity

Answer 49

sin

cos

Question 50

sin(a-b)

Answer 50

sinacosb-cosasinb

Question 51

cos(a-b)

Answer 51

cosacosb+sinasinb

Question 52

d/dx (e^x)

Answer 52

e^x

Question 53

Reciprocal Identity

1

sin

Answer 53

csc

Question 54

tana+tanb

1-tanatanb

Answer 54

tan(a+b)

Question 55

tan(a-b)

Answer 55

tana-tanb

1+tanatanb

Question 56

Pythagorean Identity

1

Answer 56

sin^2+cos^2=1

Question 57

Reciprocal Identities

sec

Answer 57

1

cos

Question 58

Reciprocol Identity

1

tan

Answer 58

cot

Question 59

Pythagorean Identity

1+tan^2=

Answer 59

sec^2

Question 60

∫tan²x dx

Answer 60

tanx - x + C

Question 61

∫cscx dx

Answer 61

-ln Icscx + cotxI + C

Question 62

∫cotx dx

Answer 62

ln IsinxI + C

Question 63

d/dx (tanx)

Answer 63

sec²x

Question 64

cosacosb-sinasinb

Answer 64

cos(a+b)

Question 65

tan(a+b)

Answer 65

tana+tanb

1-tanatanb

Question 66

cot identity

Answer 66

cos

sin

Question 67

∫sin²x dx

Answer 67

x -sin(2x)

2 4

Question 68

∫cos²x dx

Answer 68

x + sin(2x) + C

2 4

Question 69

∫ 1 dx

(a²-x²)^½

Answer 69

arcsin x + C

a

Question 70

∫ 1 dx

a²+x²

Answer 70

1 arctan x + C

a a

Question 71

Trigonometric Substitution

(a²-x²)^½

Answer 71

x=asinØ

1-sin²Ø=cos²Ø

Question 72

Trigonometric Subistution

(a²+x²)^½

Answer 72

x=atanØ

1 + tan²Ø = sec²Ø

Question 73

Trigonometric Substitution

(x²-a²)^½

Answer 73

x = asecØ

sec²Ø - 1 = tan²Ø

Question 74

Double Angle Identity

sin2x

Answer 74

2sinxcosx

Question 75

Double Angle Identity

cos2x

Answer 75

cos²x - sin²x

or

1 - 2sin²x

or

2cos²x - 1

Question 76

Double Angle Identity

tan2x

Answer 76

2tanx

1 - tan²x

Question 77

Half Angle Identity

sin²x

or

sin x

2

Answer 77

1 - cos2x

2

Question 78

Half Angle Identity

cos²x

or

cosx

2

Answer 78

1 + cos2x

2

Question 79

Half Angle Identity

tanx

2

Answer 79

sinx

1 + cosx

or

1 - cosx

sinx