4 (3)]
=
1
1
3
tan
C
2
2
–
x –
+
312
MATHEMATICS
(ii)
The given integral is of the form 7 4 (7) We write the denominator of the integrand,
32
13
10
x
x –
+
 =
2
13
10
3
3
3
x
x
–


+




=
2
2
13
17
3
6
6
x
–






+














(completing the square)
Thus
3
13
10
dx
x
x
2 +
−
∫
 =
2
2
31
13
17
6
6
dx
x



+
−








∫
Put 
13
6
x
t
+
= Then dx = dt