Primitive of Cosine Integral Function

Theorem

 * $\ds \int \map \Ci x \rd x = x \map \Ci x + \sin x + C$

where:
 * $\Ci$ denotes the cosine integral function
 * $x$ is a strictly positive real number.

Proof
By Derivative of Cosine Integral Function, we have:


 * $\ds \frac \d {\d x} \paren {\map \Ci x} = -\frac {\cos x} x$

So: