Summary sin and cos integrals

Integral Calculus Formula Sheet
Derivative Rules:

d d
dx
c   0
dx
 x n   nx n 1
d d
 sin x   cos x  cos x    sin x
dx
d
dx
d
d x
 a   a x ln a
 sec x   sec x tan x  csc x    csc x cot x dx
dx
d
dx
d
d x
e   ex
 tan x   sec2 x  cot x    csc 2 x dx
dx dx
d d d d d
cf  x    c f  x   f  x   g  x    f  x     g  x  
dx dx dx dx dx
 f g d
f  g   f   g  f  g 
f

g
 

  fg 
g2 dx
    
f g x   f  g x  g  x 



Properties of Integrals:


 kf (u )du  k  f (u )du   f (u )  g (u )du   f (u )du   g (u )du
a b a

 f ( x)dx  0
a
 f ( x)dx    f ( x)dx
a b
c b c b
1
 f ( x)dx   f ( x)dx   f ( x)dx
a a b
f ave 
b  a a
f ( x) dx
a a a


a

f ( x)dx  2 f ( x) dx if f(x) is even
0

a
f ( x) dx  0 if f(x) is odd

b f (b )

 g ( f ( x)) f ( x)dx  
a f (a)
g (u )du  udv  uv   vdu

Integration Rules:


 du  u  C  sin u du   cos u  C du 1 u
a
n 1
 arctan    C
n u
 u du  n  1  C  cos u du  sin u  C u
2 2
a a
 sec u du  tan u  C u
2
du
du
 u  ln u  C  a 2  u 2  arcsin  a   C
 csc u   cot u  C
2


 e du  e  C u
u u
du 1
 csc u cot u du   csc u  C  u u 2  a 2  a arc sec  a   C
1
 a du  ln a a C  sec u tan u du  sec u  C
u u