Rational Function If
is expressed by the fraction of polynomials, then we say
is a rational function of
and
.
Sum of Squares Let be such that hypoteneus represents a sum of squares.
DIfference of Squares Let be such that adjacent represents the difference of squares.
Integration of Irrational Functions Suppose that is a rational function of
and
. Then
1.
Let
. Then we can get integration of rational function.
[2]
1. after completing the square. Then let
By substitution, integration of irrational function should be expressed by integration of rational function.
SOLUTION
1. Let
. Then
and
. Thus
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This problem should be solved by taking
,
. But to show how nice to use a trigonometric substitution, we solve this by trinometric substitution.
SOLUTION
1. Let
. Then
,
. Thus,
Note that when
, then we do not express
. Instead,
and
.
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Exercise3-12-2. |
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.
Let
.
.
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Exercise A
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Exercise B
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