int(exp(x^n),x) and Ei

[Thomas D. Dean]

Wolfram gives the result of

integrate(exp(x^n),x) as

integrate(exp(x^n),x) = -x*Ei[(n-1)/n](-x^n)/n

http://integrals.wolfram.com/index.jsp?expr=exp(x^n)&random=false

Maple just returns the original expression.

How do I get the Ei form?

Tom Dean

[Axel Vogt]

There should be no integration variable in the result.

[G. A. Edgar]

In article <0q6dnULAAoXiA43S...@megapath.net>, Thomas D.

I think you cannot do that in Maple. That E with subscript is just a
re-writing of the original integral anyway... and Maple does not
include that variant. Using an actual value for n, Maple can produce
the incomplete Gamma versions...

integrate(exp(x^7),x)
after simplifying gets me to
(1/7)*exp(-((1/7)*I)*Pi)*(GAMMA(1/7)-GAMMA(1/7, -x^7))
and you can of course adjust the constant of integration.
So, interestingly, both Maple and Alpha use complex numbers to
represent this real integral.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/

[Peter Pein]

convert("-x*Ei[(n-1)/n](-x^n)/n", FromMma);

[G. A. Edgar]

In article <jeslnl$8f4$1...@online.de>, Peter Pein <pet...@dordos.net>
wrote:

maybe...

convert("-x*Ei[(n-1)/n,-x^n]/n", FromMma);

But even if Maple returns something, it doesn't know what it is.