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SolveAnExponentialTimesATrigonometricOverLinears​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

 Method (no overloads)

Summary

An exponential of a linear times sines and cosines of linears, and a polynomial, over
linears: each sine and cosine is written as exponentials, sin(c x) = (e^(i c x) - e^(-i c x))/(2i),
the product multiplied out, and every term is an exponential of a linear with a
complex rate over the linears, which SolveAnExponentialOfALinearOverAPowerOfALinear(AngouriMath.Entity,AngouriMath.Entity.Variable) and SolveAnExponentialOverSeveralLinears(AngouriMath.Entity,AngouriMath.Entity.Variable) answer with the exponential
integral of a complex argument. e^(2x) sin(x)/x is
(Ei((2 + i) x) - Ei((2 - i) x))/(2i), real where x is: the two terms are
conjugates. What by parts leaves of Si(ln(x)), under t = ln(x), is
e^t sin(t)/t. Rubi's 8.4, (e x)^m Si(d (a + b ln(c x^n))), answers the same way.
https://github.com/asc-community/AngouriMath/issues/1501

Remarks

Only with an exponential of a real rate beside the sine or cosine: alone over a linear,
the sine and cosine integrals are their closed form, and the rule for them answers.

























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