AngouriMath
SolveAnExponentialOfALinearOverAPowerOfALinear(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
A polynomial times an exponential of a linear over a whole power of a linear:
P(x) F^(a + b x)/(c + d x)^n , onto the exponential integral. Under
u = c + d x , F^(a + b x) is F^(a - b c/d) e^(k u) with k = b ln F/d ,
andP a polynomial in u , so every term is u^m e^(k u) : elementary for
m >= 0 , Ei(k u) for m = -1 , and below that
e^(k u) u^(m + 1)/(m + 1) - k/(m + 1) times the one above, by parts. Rubi's 2.3,
F^(c (a + b x))/(d + e x)^n and e^(-a - b x) (a + b x)^3/x^n .
https://github.com/asc-community/AngouriMath/issues/1501
and
https://github.com/asc-community/AngouriMath/issues/1501
Remarks
Only where some term's power is negative: without one the product is elementary, and the
rules for a polynomial times an exponential answer it.
rules for a polynomial times an exponential answer it.
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