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1
Review of Integration Techniques
Math 192  Spring 1997
Written by Don Allers; Revised by Sean Carver
1 Methods of Integration
Substitution
Idea:
Rename an ugly piece of the integrand and see if it reduces to a simpler form that you can
integrate.
When?
Try this method if your integral has ugly pieces like
e
tan
v
or cos(ln
x
), or if it looks like
substitution will turn the integral into an easy one, such as
R
x
n
dx
,
R
e
x
dx
, or any of the other known
integrals in
Table 7.1
on page 556.
Eg:
(a)
Z
e
tan
v
sec
2
v dv,
(b)
Z
dx
x
cos(ln
x
)
,
(c)
Z
2
√
w
dw
2
√
w
,
(d)
Z
dx
√
x
(
√
x
+ 1)
.
Integration By Parts
When?
R
f
(
x
)
g
(
x
)
dx
where
f
(
x
) can be easily diFerentiated, and
g
(
x
) easily integrated. Good
choices for
f
(
x
) are
f
(
x
) =
a
0
+
a
1
x
+
···
a
n
x
n
(any polynomial),
f
(
x
) = ln(
x
), or
f
(
x
) = tan

1
(
x
) (or
any other inverse trig function). Often
g
(
x
) is either sin(
x
), cos(
x
), or
e
x
, but
g
(
x
) can be anything if
f
(
x
) is a log function or an inverse trig function.
Method:
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This test prep was uploaded on 09/26/2007 for the course MATH 1920 taught by Professor Pantano during the Fall '06 term at Cornell University (Engineering School).
 Fall '06
 PANTANO
 Math, Calculus, dx, Sean Carver, dx dx form

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