Ch 5 Identities

Question 0

∫du

Answer 0

u+C

Question 1

∫kf(u)du

Answer 1

K∫f(u)du

Question 2

∫du/u or ∫1/u(du)

Answer 2

Ln|u|+C

Question 3

∫[f(u)+/-g(u)]du

Answer 3

∫f(u) +/- ∫g(u)

Question 4

∫u^n du

Answer 4

(U^n+1)/n+1

Question 5

∫e^udu

Answer 5

e^u + C

Question 6

∫a^udu

Answer 6

(1/lna)a^u + C

Question 7

∫sinudu

Answer 7

-cosu + C

Question 8

∫cosudu

Answer 8

Sinu + C

Question 9

∫tanudu

Answer 9

-ln |cosu| + C

Question 10

∫cotudu

Answer 10

Ln|sinu| + C

Question 11

∫secudu

Answer 11

ln |secu +tanu| + C

Question 12

∫cscudu

Answer 12

-ln |cscu +cotu| + C

Question 13

∫sec^2udu

Answer 13

Tanu + C

Question 14

∫csc^2udu

Answer 14

-cotu + C

Question 15

∫secutanudu

Answer 15

Secu + C

Question 16

∫cscucotudu

Answer 16

-cscu + C

Question 17

d/dx(cu)

Answer 17

cu`

Question 18

d/dx(sinu)

Answer 18

(Cosu)u`

Question 19

d/dx(cosu)

Answer 19

-(Sinu)u`

Question 20

d/dx(tanu)

Answer 20

(Sec^2u)u`

Question 21

d/dx(cotu)

Answer 21

-(Csc^2u)u`

Question 22

d/dx(secu)

Answer 22

(Secutanu)u`

Question 23

d/dx(cscu)

Answer 23

-(Cscucotu)u`

Question 24

d/dx(u +/- v)

Answer 24

u +/- v

Question 25

d/dx(uv)

Answer 25

uv+vu

Question 26

d/dx(u/v)

Answer 26

uv - vu/ v^2

Question 27

d/dx(c)

Answer 27

0

Question 28

d/dx(u^n)

Answer 28

nu^n-1(u`)

Question 29

d/dx(x)

Answer 29

1

Question 30

d/dx(|u|)

Answer 30

(u/|u|)(u`)

Question 31

d/dx(lnu)

Answer 31

u`/u

Question 32

d/dx(e^u)

Answer 32

e^u(u`)

Question 33

d/dx(loga u)

Answer 33

u`/(u)(lna)

Question 34

d/dx(a^u)

Answer 34

(a^u)(lna)(u`)

Question 35

d/dx(arcsinu)

Answer 35

u’/√1-u^2

Question 36

d/dx(arccosu)

Answer 36

-u’/√1-u^2

Question 37

d/dx(arctanu)

Answer 37

u`/1+u^2

Question 38

d/dx(arccotu)

Answer 38

-u`/1+u^2

Question 39

d/dx(arcsecu)

Answer 39

u’/|u|√[(u^2)-1]

Question 40

d/dx(arccscu)

Answer 40

-u’/|u|√[(u^2)-1]

Question 41

∫du/√[(a^2)-(u^2)] or ∫1/√[(a^2)-(u^2)] (du)

Answer 41

arcsin(u/a) + C

Question 42

∫du/(a^2)-(u^2)

Answer 42

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

Question 43

∫du/u√[(u^2)-(a^2)]

Answer 43

(1/a)arcsec(|u|/a) + C