sind udx

(cos ) 'u u

cosd udx

(sin ) 'u u

tand udx

2(sec ) 'u u

cotd udx

2(csc ) 'u u

cscd udx

(csc cot ) 'u u u

nd udx

1( ) 'nn u u

d cdx

0

d udx v

2

' 'vu uvv

d u vdx

' 'u v v u

d udx

( '), 0u u uu

ud edx

'ue u

lnd udx

'uu

logad udx

'

lnua u

ud adx

ln 'ua a u

arcsind udx

2

'

1

u

u

arccosd udx

2

'

1

u

u

arctand udx

2

'1uu

arccotd udx

2

'1uu

arcsecd udx

2

'

1

u

u u

arccscd udx

2

'

1

u

u u

d xdx

1

d u vdx

' 'u v

d cudx

'cu

( )kf u du

( )k f u du

[ ( ) ( )]f u g u du

( ) ( ) f u du g u du

du

u C

nu du

1

1

nu Cn

duu

ln u C

ue du

ue C

sin u du

cosu C

cos u du

sinu C

2sec u du

tanu C

2csc u du

cotu C

csc cot u u du

cscu C

sec tan u u du

secu C

cot u du

ln sinu C

tan u du

ln cosu C

csc u du

ln csc cotu u C

sec u du

ln sec tanu u C

ua du

1ln

ua Ca

2 2 du

a u

arcsin u Ca

2 2 du

u u a

1 arcsecu

Ca a

2 2 duu a

1 arctan u Ca a

1

n

i

c

cn

1

n

i

i

12

n n

2

1

n

i

i

1 2 16

n n n

3

1

n

i

i

22 14

n n

Fundamental Theorem of Calculus

( )b

a

f x dx

( ) ( ) ( )b

aF x F b F a

2nd Fundamental Theorem of Calculus

( )x

a

d f t dtdx

( )f x

Mean Value TheoremThere exists x=c such that

( )b

a

f x dx

( ) ( )f c b a

1 ( )b

a

f x dxb a

Average Value (Average Height of

area)

Definition of the Natural Logarithmic Function

1

1 , 0x

dt xt

ln x

Definition of exponential function base a

xa =

(ln )a xe

Definition of logarithmic function base a

alog x

1 lnln

xa

1lim 1x

x x

e

rtA Pe

Account with continuous interest

1ntrA P

n

Account with interest compounded “n” times

a year