Can I Integrate e^[1 / (1 + t)] dt Numerically?

[irony of truth]

How do I integrate this? e^[1 / (1 + t)] dt?

 

[arildno]

Short answer: Numerically.
There exist no nice anti-derivative to this function.

 

[irony of truth]

I see... so this could be the same case as that of (sinx / x) dx...

 

[dextercioby]

Long answer:
\allowbreak \left( 1+x\right) e^{\frac 1{1+x}}+\func{Ei}\left( 1,-\frac 1{1+x}\right) +C

Daniel.

 

[dextercioby]

I see... so this could be the same case as that of (sinx / x) dx...

Yes,there is a connection between Ei (exp.integral) and Si (sinus integral).

Daniel.

P.S.Chack the wolfram site for more.

 

[arildno]

Long answer:
\allowbreak \left( 1+x\right) e^{\frac 1{1+x}}+\func{Ei}\left( 1,-\frac 1{1+x}\right) +C

Daniel.

I'd rather say apparently short answer..

 

[dextercioby]

Yes,"apparently" is a well placed word...

Daniel.

P.S.Anyways,the # of characters from the code is much bigger than the # of letters from "numerically"...