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anonymous
 one year ago
Primitive !
anonymous
 one year ago
Primitive !

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}^{}e^\frac{ 1 }{ t }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1436757696187:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle \int e^{1/t}~dt }\) \(\large\color{black}{ \displaystyle u=1/t }\) \(\large\color{black}{ \displaystyle du=1/t^2~dt }\) \(\large\color{black}{ \displaystyle t^2~du=dt }\) \(\large\color{black}{ \displaystyle (1/u)^2~du=dt }\) \(\large\color{black}{ \displaystyle 1/u^2~du=dt }\) \(\large\color{black}{ \displaystyle \int \frac{e^{u}}{u^2}~du }\) I don't think this has an answer in term of a simple function. What I see to do instead is: \(\large\color{black}{ \displaystyle e^t=\sum_{n=0}^{\infty}\frac{t^n}{n!} }\) \(\large\color{black}{ \displaystyle e^{1/t}=\sum_{n=0}^{\infty}\frac{(1/t)^n}{n!} }\) \(\large\color{black}{ \displaystyle e^{1/t}=\sum_{n=0}^{\infty}\frac{(1)^nt^{n}}{n!} }\) \(\large\color{black}{ \displaystyle \int e^{1/t}~dt~=\int \sum_{n=0}^{\infty}\frac{(1)^nt^{n}}{n!} dt }\) \(\large\color{black}{ \displaystyle \int e^{1/t}~dt~=\sum_{n=0}^{\infty}\frac{(1)^nt^{n+1}}{~(n+1)~n!~} +C }\) and that you can simplify as: \(\large\color{black}{ \displaystyle \int e^{1/t}~dt~=\sum_{n=0}^{\infty}\frac{(1)^n}{~~t^{n1}~(n+1)~n!~} +C }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I mean if you haven't learned this technique using a series, then disregard my reply....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I agree that there's no antiderivative in terms of elementary functions. This seems relevant: http://mathworld.wolfram.com/ExponentialIntegral.html You should be able to get that if you integrate by parts. (I haven't bothered checking for myself, though.)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Oh, I have seen a post with this idea of integration by parts a certain number of times after which you arrive at an infinite series. I have done a similar thing when integrated e^x/x. (of course differentiating the 1/x) This is how I got to know the series technique, but without proving/showing using by parts every time is more convinient:D
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