which can be computed using integration by parts.
Damped Exponential Cosine Integral
See also
Cosine Integral, Exponential Decay, Fourier Transform--Lorentzian Function, Lorentzian FunctionExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Damped Exponential Cosine Integral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DampedExponentialCosineIntegral.html