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Question Number 138206 by Bekzod Jumayev last updated on 11/Apr/21

Commented by Bekzod Jumayev last updated on 11/Apr/21

$$Help?$$

Answered by mr W last updated on 11/Apr/21

$$=\int x^{\frac{1}{2}}{x}^{\frac{1}{2\times 3}}{x}^{\frac{1}{2\times 3\times 4}}{x}^{\frac{1}{2\times 3\times 4\times 5}}...dx$$$$=\int x^{\frac{1}{2}+\frac{1}{2\times 3}+\frac{1}{2\times 3\times 4}+\frac{1}{2\times 3\times 4\times 5}+...}dx$$$$=\int x^{(1+1+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+\frac{1}{5!}+...)-2}dx$$$$=\int x^{e-2}dx$$$$=\frac{x^{e-1}}{e-1}+C$$

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