relative of cosine integral
For determining of the value of the improper integral
related to the cosine integral, we think it as a function
of the parametre which we denote by . Then we can take the Laplace transform
(see the integration with respect to a parametre in the table of Laplace transforms):
Splitting the fractional expressions to http://planetmath.org/node/5812partial fractions and integrating give
As seen in the http://planetmath.org/node/10588table of Laplace transforms, the gotten expression is the Laplace transform of (N.B. ), and thus we have the result