How can Integrate of conjugate transpose in mathematica?

please help me to integrate this matrix in matematica:

0 ConjugateTranspose[u[x,t]] (u_x)[x,t]+I vx,t[x,t] 0 -ConjugateTranspose[u[x,t]] (u^(1,0))[x,t]-I vx,t[x,t] 0 0
0 0 0

u_x and v_x denote the diferentiate with respect to x.I dont know how can integrate the complex conjugate with mathematica. Thanks a lot.