Question Number 127857 by slahadjb last updated on 02/Jan/21
$$\int\sqrt{{x}}{e}^{{x}} {dx}\:\:? \\ $$
Commented by Dwaipayan Shikari last updated on 02/Jan/21
$$\int{x}^{\frac{\mathrm{1}}{\mathrm{2}}} \underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{n}} }{{n}!}{dx} \\ $$$$=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\int\frac{{x}^{{n}+\frac{\mathrm{1}}{\mathrm{2}}} }{{n}!}{dx}=\underset{{n}\geqslant\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{n}+\frac{\mathrm{3}}{\mathrm{2}}} }{{n}!\left({n}+\frac{\mathrm{3}}{\mathrm{2}}\right)}\:\: \\ $$