In the theory of control processes, it is important to be able to calculate
∫
0
∞
(
x
,
B
x
)
d
t
\smallint _0^\infty \left ( {x,Bx} \right )dt
without having to solve explicitly the differential equation
d
x
/
d
t
=
A
x
,
x
(
0
)
=
c
dx/dt = Ax, \\ x\left ( 0 \right ) = c
. A method for doing this is presented in this paper, generalizing one due to Anke for
n
n
th order linear differential equations.