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Question Number 147444 by aliibrahim1 last updated on 20/Jul/21

Answered by SEKRET last updated on 21/Jul/21

$$\int {\mathbf{x}}^{\frac{1}{2}}\cdot {\mathbf{x}}^{\frac{1}{2\cdot 3}}\cdot {\mathbf{x}}^{\frac{1}{2\cdot 3\cdot 4}}\cdot ....\mathbf{dx}=$$$$\int {\mathbf{x}}^{\frac{1}{2}+\frac{1}{2\cdot 3}+\frac{1}{2\cdot 3\cdot 4}+}...\mathrm{d}\mathbf{x}=\int {\mathbf{x}}^{\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+..}\mathbf{dx}$$$$\mathbf{n}=1\to \frac{\mathbf{n}}{0!}+\frac{\mathbf{n}}{1!}+\frac{\mathbf{n}}{2!}+\frac{\mathbf{n}}{3!}+...={\mathbf{e}}^{\mathbf{n}}$$$$\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+..=\mathbf{e}-2$$$$\int {\mathbf{x}}^{\mathbf{e}-2}\mathbf{dx}=\frac{{\mathbf{x}}^{\mathbf{e}-1}}{\mathbf{e}-1}+\mathbf{C}$$$$\mathbf{ABDULAZIZ}\mathbf{ABDUVALIYEV}$$$$$$$$$$

Commented by aliibrahim1 last updated on 21/Jul/21

$$thxsiramazing$$

Commented by SEKRET last updated on 21/Jul/21

$$\mathbf{not}\mathbf{at}\mathbf{all}$$

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