Integral Calculus Formula Sheet
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4Integral Calculus Formula Sheet
Derivative Rules:
d
d
c
x
nx
0
n
n
1
dx
dx
d
d
sin
x
cos
x
cos
x
sin
x
d
dx
dx
x
x
a
a
ln
a
d
d
dx
sec
x
sec tan
x
x
csc
x
csc cot
x
x
d
dx
dx
x
x
e
e
d
d
dx
2
2
tan
x
sec
x
cot
x
csc
x
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
d
f g fg
f
f g x
f g x
g x
f g
f
g f g
dx
g
g
2
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
f x dx
( )
f x dx
( )
a
a
b
c
b
c
b
1
f x dx
( )
f x dx
( )
f x dx
( )
f
f x dx
( )
ave
b a
a
a
b
a
a
a
a
if f(x) is even
if f(x) is odd
f x dx
( )
2
f x dx
( )
f x dx
( )
0
a
0
a
f b
( )
b
g f x f x dx
( ( )) ( )
g u du
( )
udv uv
vdu
a
f a
( )
Integration Rules:
du u C
sin
u du
cos
u C
du
1
u
n
1
u
arctan
C
cos
u du
sin
u C
n
u du
C
2
2
a
u
a
a
n
1
2
sec
u du
tan
u C
du
u
du
arcsin
C
ln
u
C
2
2
a
2
a
u
u
csc
u
cot
u C
u
u
u
du
1
e du
e
C
csc cot
u
u du
csc
u C
arc
sec
C
a
a
2
2
u u
a
1
u
u
a du
a
C
sec tan
u
u du
sec
u C
ln
a
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