Integral of (e^x)/x

- wasiqss

Integral of (e^x)/x

- schrodinger

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- anonymous

Applying the Divide rule of Derivative here..

- wasiqss

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

- wasiqss

and its integration man~

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## More answers

- anonymous

Sorry I did not read the question fully..

- anonymous

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

- wasiqss

ahaha omni in your dreams do it :P

- anonymous

We can use here Integration by Parts...

- anonymous

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

- wasiqss

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

- anonymous

term by term integration of the infinite series?

- anonymous

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

- anonymous

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

- anonymous

Wasi, what calculus are you in

- anonymous

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

- wasiqss

keep thinking :P

- wasiqss

hint it can be done by parts

- anonymous

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

- wasiqss

well outkas do it by parts i wanna see

- anonymous

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..

- wasiqss

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

- anonymous

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

- anonymous

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

- anonymous

in otherword let dv = -1/x^2

- wasiqss

haha outkas right :D :D

- anonymous

then add the integrals and divide by 2

- wasiqss

it is a two step integral

- wasiqss

@Omniscience poor you :P

- wasiqss

outkas which calculus you doing

- anonymous

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

- wasiqss

im good at D.E's :D

- anonymous

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

- wasiqss

calc 3 sucks!

- anonymous

indeed it does

- wasiqss

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

- anonymous

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

- anonymous

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

- wasiqss

i just cleared the first year only :/

- wasiqss

now i will go to second

- anonymous

good try mukushla :)

- anonymous

tnx

- anonymous

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

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