In[]:=
Clear["Global`*"]​​​​p[x_]:=A1*Exp[-x/l]+A2*Exp[x/l];​​u[x_]:=A3+A4*x-(h/c)*(A1*Exp[-x/l]+A2*Exp[x/l]);​​​​eqn3=μ''[x]+(q/ϵ)*p'[x]-μ[x]/λ^2+(1/λ^2)*(μhat+α*u'[x])==0;​​μ=FullSimplify[DSolveValue[eqn3,μ,x]];​​​​eqn9=c*u'[(w/2)]+h*p'[(w/2)]+(α/β)*(μ[(w/2)]-μhat-α*u'[(w/2)])==σ;​​eqn4=h*u'[(w/2)]+b*p'[(w/2)]==0;​​eqn5=h*u'[-(w/2)]+b*p'[-(w/2)]==0;​​eqn6=u[0]==0;​​eqn7=μ[(w/2)]==μ1;​​eqn8=μ[-(w/2)]==μ0;​​​​{a1,a2,a3,a4,a5,a6}=SolveValues[{eqn9,eqn4,eqn5,eqn6,eqn7,eqn8},{A1,A2,A3,A4,C[2],C[1]}];​​​​mu=μ/.{A1->a1,A2->a2,A3->a3,A4->a4,C[1]->a5,C[2]->a6};​​​​c[x_]:=c0+(1/β)*(mu[x]-μhat-α*u'[x]);​​​​c[x]​​​​K=1/((1/w)*Integrate[1/(γ*c[x]),{x,-(w/2),-(w/2)}])​​​​ComplexExpand[K]​​​​
Set
:Lists {a1,a2,a3,a4,a5,a6} and 
w
2l

hl(αμ1-αμhat-βσ)
(1+
Power[2]w

)b
2
α
-bcβ+
2
h
β
,-
w
2l

hl(αμ1-αμhat-βσ)
(1+
1

)b
2
α
-bcβ+
2
h
β
,0,-1,
1

1(11
27
,
-
w
2l
-
1
2
w(Times[2]+Power[2])-
w(l+λ)
2lλ

2bc
Times[3]+3

2
l
2
α
ϵμ0+12+26μ0+174
2c(1+
Power[2]w

)(-1+
2wPower[2]

)-b
2
α
+bcβ-
2
h
βϵ(l-λ)(l+λ)
 are not the same shape.
Out[]=
c0+
1
β
a6
-
x
λ

+a5
x/λ

-A4-
h-
A1
-
x
l

l
+
A2
x
l

l
c
α-μhat+
1
2cϵ(-l+λ)(l+λ)
-
x
λ
-
x(l+λ)
lλ

a2
2x
l
+
2x
λ

hlαϵ-a1
2x
λ

hlαϵ-a1
x-
1
l
+
1
λ
+
x(l+λ)
lλ

hlαϵ+a2
2x
l
+x-
1
l
+
1
λ
+
x(l+λ)
lλ

hlαϵ-a4c
x
l
+
2x
λ

2
l
αϵ-a4c
x
l
+x-
1
l
+
1
λ
+
x(l+λ)
lλ

2
l
αϵ+a2
2x
l
+
2x
λ

hαϵλ+a1
2x
λ

hαϵλ-a1
x-
1
l
+
1
λ
+
x(l+λ)
lλ

hαϵλ-a2
2x
l
+x-
1
l
+
1
λ
+
x(l+λ)
lλ

hαϵλ-a2c
2x
l
+
2x
λ

lq
2
λ
+a1c
2x
λ

lq
2
λ
+a1c
x-
1
l
+
1
λ
+
x(l+λ)
lλ

lq
2
λ
-a2c
2x
l
+x-
1
l
+
1
λ
+
x(l+λ)
lλ

lq
2
λ
+a4c
x
l
+
2x
λ

αϵ
2
λ
+a4c
x
l
+x-
1
l
+
1
λ
+
x(l+λ)
lλ

αϵ
2
λ
-a2c
2x
l
+
2x
λ

q
3
λ
-a1c
2x
λ

q
3
λ
+a1c
x-
1
l
+
1
λ
+
x(l+λ)
lλ

q
3
λ
+a2c
2x
l
+x-
1
l
+
1
λ
+
x(l+λ)
lλ

q
3
λ
-c
x
l
+
2x
λ

2
l
ϵμhat-c
x
l
+x-
1
l
+
1
λ
+
x(l+λ)
lλ

2
l
ϵμhat+c
x
l
+
2x
λ

ϵ
2
λ
μhat+c
x
l
+x-
1
l
+
1
λ
+
x(l+λ)
lλ

ϵ
2
λ
μhat
Power
:Infinite expression
1
0
encountered.
Out[]=
ComplexInfinity
Out[]=
ComplexInfinity