## wasiqss 3 years ago Integral of (e^x)/x

1. waterineyes

Applying the Divide rule of Derivative here..

2. wasiqss

lol water do it by that way i will give you thousand medals :P

3. wasiqss

and its integration man~

4. waterineyes

Sorry I did not read the question fully..

5. Omniscience

$\large \int\limits\frac{e^{x}}{x} dx$?? looks like cant be solved by elementary methods..

6. wasiqss

ahaha omni in your dreams do it :P

7. waterineyes

We can use here Integration by Parts...

8. Omniscience

http://www.wolframalpha.com/input/?i=integrate+%28e^x%29%2Fx like srsly? how can you solve it?

9. wasiqss

hahahah omni i heard you saying i own calculus ? :P

10. Omniscience

term by term integration of the infinite series?

11. Omniscience

hi water , have you heard of exp x = $x + x ^{2}/2! + x ^{3}/3! + x ^{4}/4!.........$

13. Outkast3r09

Wasi, what calculus are you in

if you know this then u can substitute exp x by the above and further see if its solvable !

15. wasiqss

keep thinking :P

16. wasiqss

hint it can be done by parts

17. Outkast3r09

i know it can be done by parts however are you in calculus 2

18. wasiqss

well outkas do it by parts i wanna see

19. waterineyes

For convenience, 1/x is the first function.. e^x as second function.. $\int\limits_{}^{}(\frac{1}{x}).e^x.dx = \frac{1}{x}.e^x - \int\limits_{}^{}(\frac{-1}{x^2}.e^x).dx$ $= \frac{e^x}{x} +\int\limits_{}^{} \frac{e^x}{x^2}.dx$ But now x will move on increasing like x^3, x^4 etc etc..

20. wasiqss

yeah now you have to do integration of (e^x)/x^2 right?

21. Outkast3r09

yes however switch the u and dv to go back and then add them and divide by 2

22. waterineyes

Right but that will lead to x^3 then this process continues..

23. Outkast3r09

in otherword let dv = -1/x^2

24. wasiqss

haha outkas right :D :D

25. Outkast3r09

then add the integrals and divide by 2

26. wasiqss

it is a two step integral

27. wasiqss

@Omniscience poor you :P

28. wasiqss

outkas which calculus you doing

29. Outkast3r09

I'm don with calculus, I'm in Differential Equations right now

30. wasiqss

im good at D.E's :D

31. Outkast3r09

however i don't remember hardly anything from calc 3.. and i wouldn't remember the series i it weren't for review

32. wasiqss

calc 3 sucks!

33. Outkast3r09

indeed it does

34. wasiqss

D.E are real good, in which uni you are and which year?

35. Outkast3r09

nothing like drawing 3d objects on a 2d piece of paper

36. Outkast3r09

i'm a at a community and it's around my second/3rd year

37. wasiqss

i just cleared the first year only :/

38. wasiqss

now i will go to second

good try mukushla :)

40. mukushla

tnx

41. mukushla

there was a little mistake in my answer $\int\limits \frac{e^x}{x}dx=\int\limits \frac{1}{x} \sum_{n=0}^{\infty} \frac{x^n}{n!}dx=\sum_{n=0}^{\infty} \int\limits \frac{x^{n-1}}{n!} dx=\ln x+\sum_{n=1}^{\infty} \frac{x^{n}}{n.n!}$