# Help with integral question

1. Jan 30, 2008

### bassota

hey. i got an integral:
INT = integral

INT (e^-x)/x dx

2. Jan 30, 2008

### ice109

make a substitution

3. Jan 30, 2008

### bassota

sorry, but i do not see how will a substitution help. i ahve tried it. i have also tried the integration by part and did not get anywhere. please explain, and show some details. thanks

4. Jan 30, 2008

### sutupidmath

i do not think this has any nice solution, i mean in terms of any elementary function. I believe it does not have any closed form, unless we want to expand the function under integral sign using power series, and then integrate term per term, we would get an approximation of it. Use this link http://mathworld.wolfram.com/ExponentialIntegral.html

Last edited: Jan 30, 2008
5. Jan 30, 2008

### dhris

Doesn't look like that has a representation in terms of elementary functions. Check out the exponential integral function:
http://mathworld.wolfram.com/ExponentialIntegral.html

6. Jan 31, 2008

### DanielleL5432

Can't you just use integration by parts over and over again...let u=1/x, then 1/x^2, etc and keep letting dv=e^-x dx?

7. Jan 31, 2008

### dhris

Ha, you beat me to it. Can you believe it took me at least 6 minutes to write my two-line post?

Sure, but what does that get you?

8. Jan 31, 2008

### HallsofIvy

Staff Emeritus
Yes, that would give you an infinite series solution.

I think it would be easier to start with an infinite series:
$$e^{-x}= 1- x+ \frac{1}{2}x^2- \cdot\cdot\cdot\+ \frac{(-1)^n}{n!}x^n+\cdot\cdot\codt$$
so
$$\frac{e^{-x}}{x}= \frac{1}{x}- 1+ \frac{1}{2}x- \cdot\cdot\cdot\+ \frac{(-1)^n}{n!}x^{n-1}+\cdot\cdot\codt$$

Integrate that to get an infinite series solution.

9. Jan 31, 2008

### sutupidmath

Wouldn't he need firs to determine whether this series converges uniformly, and whether they fullfill some other conditions which i do not actually know exactly which are they? Or it is obvious that this series can be integrated term by term?

P.S. Pardone my ignorance!