Astronomical Applications Department, U.S. Naval Observatory Sensitivity Integral Page 25
d
1
2
(
)
factor

(
)
expansion
,
,
integrand
1
[
]
,
s r
6
(
)
expansion
,
,
integrand
1
[
]
,
s r
4
x
(
)
select
,
,
has
(
)
op
,
1 %
g
2
r
2
=
(
)
applyop
,
,
, ,
collect
(
)
location
,
%% %
%% s factor
d
1
2
(
)
factor
(
)
expansion
,
,
integrand
1
[
]
,
s r
4
x
=
d
1
2

1
3
s
2
x
6
r
2
(
)
 +
1
g
2
(
)
+
s
2
r
2
(
)
+ +
g
2
g
1
(
)
+
+
+
+
a
0
a
1
x
a
2
x
2
a
3
x
3
a
4
x
4
x
d
1
2
(
)
+
+
+
+
a
0
a
1
x
a
2
x
2
a
3
x
3
a
4
x
4
x
4
(
)
 +
1
g
2
r
2
s
2
x
Remove the geometry terms to the outside of the integrals, for convenience
collecting them into the quantity
=
Q
+
s
2
r
2
(
)
+ +
g
2
g
1
.
(
)
simplify
,
% {
}
=
+
s
2
r
2
(
)
+ +
g
2
g
1
Q
(
)
factor
(
)
combine
,
% Int
=
d
1
2

Q x
6
(
)
+
+
+
+
a
0
a
1
x
a
2
x
2
a
3
x
3
a
4
x
4
x
d
1
2
3 x
4
(
)
+
+
+
+
a
0
a
1
x
a
2
x
2
a
3
x
3
a
4
x
4
x
Evaluate the integrals and substitute
=

2
1
1
as before. We find the result
Page 25