University of Toronto, MAT 137Y
A Note About Integration Techniques for Term Test 3
One of the most common questions asked is whether one is responsible for memorizing the table of
integrals that is provided in the front and back covers of the text. The answer is obviously no; the
basic strategy is to apply the techniques of integration which reduces the integral to one or more
basic integrals which you have memorized. A table of integrals will NOT be provided for the test.
The following integrals are ones that should be memorized. The constants of integration have been
omitted.
Table of Basic Integration Formulas
1
.
Z
x
n
dx
=
x
n
+
1
n
+
1
(
n
=

1
)
2
.
Z
1
x
dx
=
ln

x

3
.
Z
e
x
dx
=
e
x
4
.
Z
a
x
dx
=
a
x
ln
a
5
.
Z
sin
xdx
=

cos
x
6
.
Z
cos
xdx
=
sin
x
7
.
Z
sec
2
xdx
=
tan
x
8
.
Z
csc
2
xdx
=

cot
x
9
.
Z
sec
x
tan
xdx
=
sec
x
10
.
Z
csc
x
cot
xdx
=

csc
x
11
.
Z
sec
xdx
=
ln

sec
x
+
tan
x

12
.
Z
csc
xdx
=
ln

csc
x

cot
x

13
.
Z
tan
xdx
=
ln

sec
x

14
.
Z
cot
xdx
=
ln

sin
x

15
.
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 Spring '10
 unknown
 Integrals, dx, Basic integration formulas

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