In[]:=
m[x_]=ArcCos
1
4
1-d

1-d
+
1+d
+
1-d
-
1+d
Cos[g*x]+
1
4
1+d

1-d
+
1+d
+-
1-d
+
1+d
Cos[g*x]​​n[x_]=Sqrt-18-1+
1-
2
d
(2
2
g
+
2
w
-
2
w
Cos[2g*x])​​k[y_]:=Manipulate[NIntegrate[n[t],{t,0,y}],{g,0,20},{w,0,2Pi}]​​Manipulate[Plot[k[x],{x,0,10}],{g,0,20},{w,0,2Pi}]
Out[]=
ArcCos
1
4
1-d

1-d
+
1+d
+
1-d
-
1+d
Cos[gx]+
1
4
1+d

1-d
+
1+d
+-
1-d
+
1+d
Cos[gx]
Out[]=
--1+
1-
2
d
(2
2
g
+
2
w
-
2
w
Cos[2gx])
2
2
Out[]=
​
g
w
2
4
6
8
10
-1.0
-0.5
0.5
1.0
In[]:=
Manipulate[Plot[x*m[x]/k[x],{x,0,10}],{d,0,1},{g,0,20},{w,0,2Pi}]
Out[]=
​
d
g
w
2
4
6
8
10
-1.0
-0.5
0.5
1.0