FullSimplifyIntegrate
2
L
*Sin
2*π*q*x
L
+ϕ1*Sin
2*π*q*x
L
+ϕ2*Sin
2*π*qt*x
L
+ϕ3,{x,0,L},Element[q|qt,Integers]
0
FullSimplifyIntegrate
2
L
*Sin
2*π*q*x
L
+ϕ1*Sin
2*π*q*x
L
+ϕ2*Sin
2*π*qt*x
L
+ϕ3/.{qt2*q},{x,0,L},Element[q|qt,Integers]
1
2
Sin[ϕ1+ϕ2-ϕ3]