integral
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how can i do inte for this complicate equation ,
f_N (t)=ρ(1+C_A)A u+1/2 ρC_D Dv|v|
V=πH/T*(sinh[k(z+d)])/(sinh(kd)) cos(kx-ωt)
u=(2π^2∗H)/T^2 *(cosh[k(z+d)])/(sinh(kd)) sin(kx-ωt)
my code
syms p c A H T k z d x w t c2 v u
% Define symbolic expressions for v and u
v_expr = -(H/2)*(cosh(k*(z+d))/sinh(k*d))*sin(k*x-w*t);
u_expr = ((2*pi^2*H)/T^2)*(cosh(k*(z+d))/sinh(k*d))*sin(k*x-w*t);
% Define f using the symbolic expressions for v and u
f = p*(1+c)*A*u_expr + (1/2)*p*c2*v_expr*abs(v_expr);
% Compute the integral of f with respect to z
F = int(f,z)
but ,matlab show the answer i coudnt understand
F =
piecewise(H == 0 | cosh(k*(d + z)) == 0 | in((k*x - t*w)/pi, 'integer'), -(A*H*p*sin(k*x - t*w)*sin(k*(d + z)*1i)*(c + 1)*2778046668940015i)/(140737488355328*T^2*k*sinh(d*k)), cosh(k*(d + z)) ~= 0 & 0 < H*sin(k*x - t*w)*cosh(k*(d + z)) & ~in((k*x - t*w)/pi, 'integer'), - (p*((4398046511104*H^2*c2*sin(k*x - t*w)^2*sinh(2*k*(d + z)))/abs(sinh(d*k)) - (2778046668940015*A*H*sin(k*x - t*w)*sinh(k*(d + z))*(c + 1))/T^2))/(140737488355328*k*sinh(d*k)) - (H^2*c2*p*sin(k*x - t*w)^2*(d + z))/(16*abs(sinh(d*k))*sinh(d*k)), cosh(k*(d + z)) ~= 0 & H*sin(k*x - t*w)*cosh(k*(d + z)) < 0 & ~in((k*x - t*w)/pi, 'integer'), (p*((4398046511104*H^2*c2*sin(k*x - t*w)^2*sinh(2*k*(d + z)))/abs(sinh(d*k)) + (2778046668940015*A*H*sin(k*x - t*w)*sinh(k*(d + z))*(c + 1))/T^2))/(140737488355328*k*sinh(d*k)) + (H^2*c2*p*sin(k*x - t*w)^2*(d + z))/(16*abs(sinh(d*k))*sinh(d*k)), ~in(H*sin(k*x - t*w)*cosh(k*(d + z)), 'real') & cosh(k*(d + z)) ~= 0 & ~in((k*x - t*w)/pi, 'integer'), int((H*p*sin(k*x - t*w)*cosh(k*(d + z))*(- 17592186044416*c2*abs(H*sin(k*x - t*w)*cosh(k*(d + z)))*T^2 + 2778046668940015*A*abs(sinh(d*k)) + 2778046668940015*A*c*abs(sinh(d*k))))/(140737488355328*T^2*abs(sinh(d*k))*sinh(d*k)), z))
