wasiqss
  • wasiqss
Integral of (e^x)/x
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Applying the Divide rule of Derivative here..
wasiqss
  • wasiqss
lol water do it by that way i will give you thousand medals :P
wasiqss
  • wasiqss
and its integration man~

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More answers

anonymous
  • anonymous
Sorry I did not read the question fully..
anonymous
  • anonymous
\[\large \int\limits\frac{e^{x}}{x} dx\]?? looks like cant be solved by elementary methods..
wasiqss
  • wasiqss
ahaha omni in your dreams do it :P
anonymous
  • anonymous
We can use here Integration by Parts...
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=integrate+%28e^x%29%2Fx like srsly? how can you solve it?
wasiqss
  • wasiqss
hahahah omni i heard you saying i own calculus ? :P
anonymous
  • anonymous
term by term integration of the infinite series?
anonymous
  • anonymous
like srsly.. http://en.wikipedia.org/wiki/Exponential_integral
anonymous
  • anonymous
hi water , have you heard of exp x = \[x + x ^{2}/2! + x ^{3}/3! + x ^{4}/4!.........\]
anonymous
  • anonymous
Wasi, what calculus are you in
anonymous
  • anonymous
if you know this then u can substitute exp x by the above and further see if its solvable !
wasiqss
  • wasiqss
keep thinking :P
wasiqss
  • wasiqss
hint it can be done by parts
anonymous
  • anonymous
i know it can be done by parts however are you in calculus 2
wasiqss
  • wasiqss
well outkas do it by parts i wanna see
anonymous
  • 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
  • wasiqss
yeah now you have to do integration of (e^x)/x^2 right?
anonymous
  • anonymous
yes however switch the u and dv to go back and then add them and divide by 2
anonymous
  • anonymous
Right but that will lead to x^3 then this process continues..
anonymous
  • anonymous
in otherword let dv = -1/x^2
wasiqss
  • wasiqss
haha outkas right :D :D
anonymous
  • anonymous
then add the integrals and divide by 2
wasiqss
  • wasiqss
it is a two step integral
wasiqss
  • wasiqss
@Omniscience poor you :P
wasiqss
  • wasiqss
outkas which calculus you doing
anonymous
  • anonymous
I'm don with calculus, I'm in Differential Equations right now
wasiqss
  • wasiqss
im good at D.E's :D
anonymous
  • 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
  • wasiqss
calc 3 sucks!
anonymous
  • anonymous
indeed it does
wasiqss
  • wasiqss
D.E are real good, in which uni you are and which year?
anonymous
  • anonymous
nothing like drawing 3d objects on a 2d piece of paper
anonymous
  • anonymous
i'm a at a community and it's around my second/3rd year
wasiqss
  • wasiqss
i just cleared the first year only :/
wasiqss
  • wasiqss
now i will go to second
anonymous
  • anonymous
good try mukushla :)
anonymous
  • anonymous
tnx
anonymous
  • 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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