Differentiation and Integration Formulas

Question 1

d(cu)

Answer 1

cu’

Question 2

d(u ± v)

Answer 2

u’ ± v’

Question 3

d(uv)

Answer 3

uv’ + vu’

Question 4

d(u/v)

Answer 4

(vu’ - uv’)/v^2

Question 5

d(c)

Answer 5

0

Question 6

d(u^n)

Answer 6

n(u^(n-1))(u’)

Question 7

d(x)

Answer 7

1

Question 8

d(abs(u))

Answer 8

u/abs(u) * (u’), u ≠ 0

Question 9

d(ln(u))

Answer 9

u’/u

Question 10

d(e^u)

Answer 10

(e^u)u’

Question 11

d(log(bs(a))u)

Answer 11

u’/(ln(a))u

Question 12

d(a^u)

Answer 12

(ln(a))(a^u)(u’)

Question 13

d(sin(u))

Answer 13

(cos(u))(u’)

Question 14

d(cos(u))

Answer 14

-(sin(u))(u’)

Question 15

d(tan(u))

Answer 15

(sec^2(u))(u’)

Question 16

d(cot(u))

Answer 16

-(csc^2(u))(u’)

Question 17

d(sec(u))

Answer 17

(sec(u)*tan(u))(u’)

Question 18

d(csc(u))

Answer 18

-(csc(u)*cot(u))(u’)

Question 19

d(arcsin(u))

Answer 19

u’/sqrt(1 - (u^2))

Question 20

d(arctan(u))

Answer 20

u’/(1+(u^2))

Question 21

∫kf(u)(du)

Answer 21

k∫f(u)(du)

Question 22

∫f(u) ± g(u)

Answer 22

∫f(u)(du) ± ∫g(u)(du)

Question 23

∫(du)

Answer 23

u + C

Question 24

∫(u^n)(du)

Answer 24

[(u^(n+1))/(n + 1)] + C, n ≠ -1

Question 25

∫(du)/u

Answer 25

ln(abs(u)) + C

Question 26

∫(e^u)(du)

Answer 26

(e^u) + C

Question 27

∫(a^u)(du)

Answer 27

[1/(ln(a)) * (a^u)] + C

Question 28

∫sin(u)(du)

Answer 28

-cos(u) + C

Question 29

∫cos(u)(du)

Answer 29

sin(u) + C

Question 30

∫tan(u)(du)

Answer 30

-ln(abs(cos(u))) + C

Question 31

∫cot(u)(du)

Answer 31

ln(abs(sin(u))) + C

Question 32

∫sec(u)(du)

Answer 32

ln(abs(sec(u) + tan(u))) + C

Question 33

∫csc(u)(du)

Answer 33

-ln(abs(csc(u) + cot(u))) + C

Question 34

∫sec^2(u)(du)

Answer 34

tan(u) + C

Question 35

∫csc^2(u)(du)

Answer 35

-cot(u) + C

Question 36

∫sec(u)tan(u)(du)

Answer 36

sec(u) + C

Question 37

∫csc(u)cot(u)(du)

Answer 37

-csc(u) + C

Question 38

∫(du)/sqrt((a^2) - (u^2))

Answer 38

arcsin(u/a) + C

Question 39

∫(du)/((a^2) + (u^2))

Answer 39

(1/a)arctan(u/a) + C

Question 40

∫(e^ku)(du)

Answer 40

[(1/k)(e^ku)] + C