Question

Integral of (e^x)/x

Answer 1

Applying the Divide rule of Derivative here..

Answer 2

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

Answer 3

and its integration man~

Answer 4

Sorry I did not read the question fully..

Answer 5

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

Answer 6

ahaha omni in your dreams do it :P

Answer 7

We can use here Integration by Parts...

Answer 8

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

Answer 9

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

Answer 10

term by term integration of the infinite series?

Answer 11

like srsly..
http://en.wikipedia.org/wiki/Exponential_integral

Answer 12

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

Answer 13

Wasi, what calculus are you in

Answer 14

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

Answer 15

keep thinking :P

Answer 16

hint it can be done by parts

Answer 17

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

Answer 18

well outkas do it by parts i wanna see

Answer 19

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..

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

in otherword let dv = -1/x^2

Answer 24

haha outkas right :D :D

Answer 25

then add the integrals and divide by 2

Answer 26

it is a two step integral

Answer 27

@Omniscience poor you :P

Answer 28

outkas which calculus you doing

Answer 29

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

Answer 30

im good at D.E's :D

Answer 31

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

Answer 32

calc 3 sucks!

Answer 33

indeed it does

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

i just cleared the first year only :/

Answer 38

now i will go to second

Answer 39

good try mukushla :)

Answer 40

tnx

Answer 41

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