wasiqss
Integral of (e^x)/x
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waterineyes
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Applying the Divide rule of Derivative here..
wasiqss
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lol water do it by that way i will give you thousand medals :P
wasiqss
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and its integration man~
waterineyes
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Sorry I did not read the question fully..
Omniscience
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\[\large \int\limits\frac{e^{x}}{x} dx\]??
looks like cant be solved by elementary methods..
wasiqss
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ahaha omni in your dreams do it :P
waterineyes
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We can use here Integration by Parts...
wasiqss
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hahahah omni i heard you saying i own calculus ? :P
Omniscience
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term by term integration of the infinite series?
meera_yadav
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hi water ,
have you heard of exp x = \[x + x ^{2}/2! + x ^{3}/3! + x ^{4}/4!.........\]
Outkast3r09
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Wasi, what calculus are you in
meera_yadav
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if you know this then u can substitute exp x by the above and further see if its solvable !
wasiqss
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keep thinking :P
wasiqss
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hint it can be done by parts
Outkast3r09
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i know it can be done by parts however are you in calculus 2
wasiqss
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well outkas do it by parts i wanna see
waterineyes
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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
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yeah now you have to do integration of (e^x)/x^2 right?
Outkast3r09
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yes however switch the u and dv to go back and then add them and divide by 2
waterineyes
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Right but that will lead to x^3 then this process continues..
Outkast3r09
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in otherword let dv = -1/x^2
wasiqss
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haha outkas right :D :D
Outkast3r09
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then add the integrals and divide by 2
wasiqss
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it is a two step integral
wasiqss
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@Omniscience poor you :P
wasiqss
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outkas which calculus you doing
Outkast3r09
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I'm don with calculus, I'm in Differential Equations right now
wasiqss
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im good at D.E's :D
Outkast3r09
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however i don't remember hardly anything from calc 3.. and i wouldn't remember the series i it weren't for review
wasiqss
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calc 3 sucks!
Outkast3r09
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indeed it does
wasiqss
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D.E are real good, in which uni you are and which year?
Outkast3r09
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nothing like drawing 3d objects on a 2d piece of paper
Outkast3r09
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i'm a at a community and it's around my second/3rd year
wasiqss
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i just cleared the first year only :/
wasiqss
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now i will go to second
meera_yadav
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good try mukushla :)
mukushla
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tnx
mukushla
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there was a little mistake in my answer
\[\int\limits \frac{e^x}{x}dx=\int\limits \frac{1}{x} \sum_{n=0}^{\infty} \frac{x^n}{n!}dx=\sum_{n=0}^{\infty} \int\limits \frac{x^{n-1}}{n!} dx=\ln x+\sum_{n=1}^{\infty} \frac{x^{n}}{n.n!}\]