If
\[
\int \frac{\cos\left(\frac{7x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\,dx
=
a\sin x+b\sin2x+c\sin^3x-dx+k,
\]
then \(a+b+c+d=\)
Show Hint
Use the identity
\[
\boxed{\frac{\cos7A}{\cos A}
=
64\cos^6A-112\cos^4A+56\cos^2A-7}
\]
and then convert powers of
\[
\cos\frac{x}{2}
\]
into multiple-angle expressions before integrating.