# Any way to evaluate such an integral

1. Nov 11, 2008

1. The problem statement, all variables and given/known data

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

Any attempts will be appreciated.

2. Nov 11, 2008

### marlon

Re: Integration

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

and then partial integration

that's my first guess...

marlon

3. Nov 11, 2008

### Staff: Mentor

Re: Integration

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.

4. Nov 11, 2008

Re: Integration

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

5. Nov 11, 2008

### Dick

Re: Integration

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.

6. Nov 12, 2008

Re: Integration

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

7. Nov 12, 2008

### CompuChip

Re: Integration

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

8. Nov 12, 2008