Math Formula Sheet
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1Differentiation Formulas
Integration Formulas
d
k = 0
(1)
dx = x + C
(1)
dx
d
+1
x
[f (x)
g(x)] = f (x)
g (x)
(2)
x dx =
+ C
(2)
dx
n + 1
d
[k f (x)] = k f (x)
(3)
dx
dx
= ln x + C
(3)
x
d
[f (x)g(x)] = f (x)g (x) + g(x)f (x) (4)
dx
e dx = e + C
(4)
d
f (x)
g(x)f (x)
f (x)g (x)
=
(5)
2
dx
g(x)
[g(x)]
1
a dx =
a + C
(5)
d
ln a
f (g(x)) = f (g(x)) g (x)
(6)
dx
d
ln x dx = x ln x
x + C
(6)
1
x = nx
(7)
dx
d
sin x = cos x
(8)
sin x dx =
cos x + C
(7)
dx
d
cos x =
sin x
(9)
cos x dx = sin x + C
(8)
dx
d
2
tan x = sec
x
(10)
dx
tan x dx =
ln cos x + C
(9)
d
2
cot x =
csc
x
(11)
dx
cot x dx = ln sin x + C
(10)
d
sec x = sec x tan x
(12)
dx
d
sec x dx = ln sec x + tan x + C
(11)
csc x =
csc x cot x
(13)
dx
d
e = e
(14)
csc x dx =
ln csc x + cot x + C (12)
dx
d
a = a ln a
(15)
2
sec
x dx = tan x + C
(13)
dx
d
1
ln x =
(16)
dx
x
2
csc
x dx =
cot x + C
(14)
d
1
1
sin
x =
(17)
dx
2
1
x
sec x tan x dx = sec x + C
(15)
d
1
1
cos
x =
(18)
dx
2
1
x
csc x cot x dx =
csc x + C
(16)
d
1
1
tan
x =
(19)
2
dx
x
+ 1
dx
x
1
d
1
= sin
+ C
(17)
1
cot
x =
(20)
2
2
a
a
x
2
dx
x
+ 1
d
1
dx
1
x
1
1
sec
x =
(21)
=
tan
+ C
(18)
2
2
dx
2
a
+ x
a
a
x
x
1
d
1
dx
1
x
1
csc
x =
(22)
1
=
sec
+ C
(19)
dx
2
x
x
1
a
a
2
2
x x
a
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