Basic Integration Rules and Properties

BASIC INTEGRATION RULES AND PROPERTIES
PROPERTIES:
1) ∫ k f ( x )dx = k ∫ f ( x )dx where k is a constant
b
3)
∫
a
2)
∫ [ f ( x) ± g ( x)] dx =∫ f ( x)dx ± ∫ g ( x)dx
a
f (x) dx = − ∫ f (x) dx
b
RULES:
1)
n
∫ x dx =
x n +1
+ C , n ≠ −1
n +1
3) ∫ e x dx = e x + C
2)
1
∫ x dx = ln x + C
4) ∫ a x dx =
ax
+C
ln a
5)
∫ sin x dx = − cos x + C
6)
∫ cos x dx = sin x + C
7)
∫ tan x dx = − ln cos x + C = ln sec x + C
8)
∫ cot x dx = ln sin x + C
9)
∫ sec x dx = ln sec x + tan x + C
10)
11)
∫ sec
13)
∫ sec x tan x dx = sec x + C
15)
∫ 1+ x
17)
∫x
2
xdx = tan x + C
1
2
dx = arctan x + C
1
x2 − 1
dx = arcsec x + C
∫ csc x dx = ln csc x − cot x
= − ln csc x + cot x
12)
∫ csc
14)
∫ csc x cot x dx = − csc x + C
16)
∫
2
xdx = − cot x + C
1
1 − x2
dx = arcsin x + C