(7)
To find the integral 
2
dx
ax
bx
c
+
+
∫
, we write
ax 2 + bx + c = 
2
2
2
2
2
4
b
c
b
c
b
a x
x
a
x
–
a
a
a
a
a








+
+
=
+
+


















Now, put 
b2
x
t
a
+
= so that dx = dt and writing 
2
2
42
c
–b
k
a
a
= ± We find the
integral reduced to the form 
2
2
1
dt
a
t
∫±k
 depending upon the sign of 
2
42
c
a–b
a






and hence can be evaluated (8)
To find the integral of the type 
2
dx
ax
bx
c
+
+
∫
, proceeding as in (7), we
obtain the integral using the standard formulae (9)
To find the integral of the type 
2
px
q
dx
ax
bx
c
++
+
∫
, where p, q, a, b, c are
constants, we are to find real numbers A, B such that
2
+
= A
(
) + B = A (2
) + B
d
px
q
ax
bx
c
ax
b
dx
+
+
+
To determine A and B, we equate from both sides the coefficients of x and the
constant terms