2 equals
9
4
dx
x
x
−
∫
(A)
–1
1
9
8
sin
C
9
8
x −
 +




(B)
–1
1
8
9
sin
C
2
9
x −
 +




(C)
–1
1
9
8
sin
C
3
8
x −
 +




(D)
–1
1
9
8
sin
C
2
9
x −
 +




7 5  Integration by Partial Fractions
Recall that a rational function is defined as the ratio of two polynomials in the form
P( )
Q( )
x
x
, where P (x) and Q(x) are polynomials in x and Q(x) ≠ 0 If the degree of P(x)
is less than the degree of Q(x), then the rational function is called proper, otherwise, it
is called improper The improper rational functions can be reduced to the proper rational
INTEGRALS         317
functions by long division process