A.7. INTEGRAL RULES 185
A.7 INTEGRAL RULES
BASIC INTEGRATION RULES
•
Z
x
n
dx D
1
n C1
x
nC1
C C
•
Z
a f .x/ dx D a
Z
f .x/ dx
•
Z
.
f .x/ C g.x/
/
dx D
Z
f .x/ dx C
Z
g.x/ dx
LOG AND EXPONENT
•
Z
1
x
dx
D
ln
.x/
C
C
•
Z
e
x
dx D e
x
C C
TRIG AND INVERSE TRIG
•
Z
sin.x/ dx D cos.x/ CC
•
Z
cos.x/ dx D sin.x/ CC
•
Z
sec
2
.x/ dx D tan.x/ CC
•
Z
csc
2
.x/ dx D cot.x/ CC
•
Z
sec.x/ tan.x/ dx D sec.x/ CC
•
Z
csc.x/ cot.x/ dx D csc.x/ CC
•
Z
1
p
1 x
2
dx D sin
1
.x/ C C
•
Z
1
1 Cx
2
dx D tan
1
.x/ C C
•
Z
1
x
p
x
2
1
dx D sec
1
.jxj/ C C
•
Z
tan.x/ dx D ln jsec.x/j C C
•
Z
sec.x/ dx D ln jsec.x/ C tan.x/j CC
INTEGRATION BY PARTS
Z
U dV D U V
Z
V dU
EXPONENTIAL/POLYNOMIAL SHORTCUT
Z
p.x/e
x
dx D
p.x/ p
0
.x/ C p
00
.x/ p
000
.x/ C
e
x
C C
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