We have
3

2		 xu1/2 du
=
3

2
u+1

2
u1/2 du
(substituting for x)
=
3

4
u3/2+u1/2 du
(simplifying)
=
3

10
u5/2
+1

2		u3/2+ C
(taking the antiderivative)
=
3

10
(2x1)5/2
+1

2		(2x1)3/2+ C
(substituting for u)