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Question Number 163828 by milandou last updated on 11/Jan/22

$$\int \frac{e^x}{x}$$

Answered by Ar Brandon last updated on 11/Jan/22

$$=\int \underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{x^{n-1}}{n!}dx=\int (\frac{1}{x}+\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{x^{n-1}}{n!})dx$$$$=\ln x+\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{x^n}{n(n!)}+C$$

Answered by essojean last updated on 20/Jan/22

$$\int \frac{e^x}{x}=Ei\left(x\right)+c$$

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