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Question Number 67937 by A8;15: last updated on 02/Sep/19

Commented by mathmax by abdo last updated on 02/Sep/19

$$atformofserie$$$$I=\int \sqrt{e^x}dx=\int e^{\frac{x}{2}}dx=\int \left(\sum _{n=0}^{\mathrm{\infty }}\frac{{\left(\frac{x}{2}\right)}^n}{n!}\right)dx$$$$=\sum _{n=0}^{\mathrm{\infty }}\frac{1}{n!2^n}\int x^{n}dx=\sum _{n=0}^{\mathrm{\infty }}\frac{x^{n+1}}{(n+1)n!2^n}+Candthis$$$$serieconvergesunif.withradiusinfinite.$$

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