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

∫(e^x /x)

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

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

=∫Σ_(n=0) ^∞ (x^(n−1) /(n!))dx=∫((1/x)+Σ_(n=1) ^∞ (x^(n−1) /(n!)))dx  =lnx+Σ_(n=1) ^∞ (x^n /(n(n!)))+C

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

Answered by essojean last updated on 20/Jan/22

∫(e^x /x)=Ei(x)+c

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

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