integrate e^x / x

Question

integrate  e^x / x

anonymous · Answer

It has no elementary form

anonymous · Answer

I was just curious if you could do it as a power series.. or is that just pushing it?

anonymous · Answer

$$\sum_{0}^{\infty} x ^{n-1} \div n!$$

anonymous · Answer

Then integrate

anonymous · Answer

yeah, but that isn't an elementary form, ie. it can't be written as a finite sum of polynomials and special functions. You could use the infinite series to approximate it but it will never have a finite form.

anonymous · Answer

Hmm alright, probably won't have to worry about it for the exam then :P

anonymous · Answer

definitely not, but if you are interested it is a form of a special function called the exponential integral denoted Ei(x). Far more integrals are not solvable than are solvable, but i doubt you'll ever be given a problem without a solution in a basic calculus class.

anonymous · Answer

MIT Prof Denis Auroux addresses the integral to this function in this lecture beginning about 42 mins http://www.youtube.com/watch?v=YP_B0AapU0c&feature=BFa&list=PL4C4C8A7D06566F38&index=16

anonymous · Answer

He is not integrating the function, he is changing the order of integration of a double integral. Just because you can rearrange in a double integral does not mean the inner integral is elementary. http://en.wikipedia.org/wiki/Exponential_integral

anonymous · Answer

I wasn't disputing your point. I was saying a very smart guy is talking about the same thing. :)