Any way to evaluate such an integral

[caduceus]

Homework Statement

Is there any way to evaluate such an integral; $$\int e^{2x}x^{-1}dx$$

Any attempts will be appreciated.

 

[marlon]

$$\int e^{2x}x^{-1}dx = \int e^{2x}dln(x)$$

and then partial integration

that's my first guess...

marlon

 

[Mark44]

I don't believe that this integral is amenable to the application of integration by parts. I tried a couple of the obvious substitutions for integration by parts, but didn't get anything that was simpler.

 

[caduceus]

and then partial integration

that's my first guess...

marlon

I guess if we proceed it, we will get back into the starting integral and can obtain no solution.

 

[Dick]

There is a special function called the 'exponential integral' that's closely related to your integral. http://en.wikipedia.org/wiki/Exponential_integral That's a pretty good sign there is no simple way to reduce that to elementary functions.

 

[icantadd]

So this integral requires a complex solution? What does that mean in terms of the geometric interpretation of integrals?

 

[CompuChip]

It's not complex, Ei is real.
What geometric interpretation (other than the usual of integral as area under a curve) would you expect?

 

[icantadd]

It's not complex, Ei is real.
What geometric interpretation (other than the usual of integral as area under a curve) would you expect?

None, now that you said Ei is real. The equation on the wiki page threw me off where it has Ei is related to E1 as follows and then it has some odd symbol I haven't seen and an i. What does the funny + looking symbol mean?