Evaluate
\left\{\begin{matrix}\frac{d\cos(x\left(d+1\right))-d\cos(x\left(1-d\right))-\cos(x\left(d+1\right))-\cos(x\left(1-d\right))}{2\left(1-d^{2}\right)}+С,&|d|\neq 1\\-\frac{\left(\cos(x)\right)^{2}}{2}+С,&|d|=1\end{matrix}\right.
Differentiate w.r.t. x
\left\{\begin{matrix}\frac{\sin(x\left(d+1\right))+\sin(x\left(1-d\right))}{2},&|d|\neq 1\\\frac{\sin(2x)}{2},&|d|=1\end{matrix}\right.
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