Also
( )
d
k
f x dx
dx




∫
 =  
( )
=
( )
kd
f x dx
k f x
dx ∫
 Therefore, using the Property (II), we have 
( )
( )
k f x dx
k
f x dx
=
∫
∫ (V)
Properties (III) and (IV) can be generalised to a finite number of functions
f1, f2, , fn and the real numbers, k1, k2, , kn giving
[
]
1 1
2 2
( )
( )
( )
n
n
k f x
k f
x