24 2
equals
2
2
dx
x
+x
+
∫
(A)
x tan–1 (x + 1) + C
(B)
tan–1 (x + 1) + C
(C)
(x + 1) tan–1x + C
(D)
tan–1x + C
25 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