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Question Number 60791 by arcana last updated on 25/May/19

$$\int \frac{e^n}{x^{n+1}}dx,\mathrm{n}\in \mathbb{N}$$

Commented by Forkum Michael Choungong last updated on 25/May/19

$$\int \frac{e^n}{x^{n+1}}dx=e^n\int \frac{1}{x^{n+1}}dx$$$$=-e^n\left(\frac{1}{{nx}^n}\right)wheren\in \mathbb{N}$$$$$$$$$$

Commented by arcana last updated on 25/May/19

$$\mathrm{thanks}$$

Answered by MJS last updated on 25/May/19

$$\int \frac{{\mathrm{e}}^n}{x^{n+1}}dx={\mathrm{e}}^n\int \frac{dx}{x^{n+1}}=-\frac{{\mathrm{e}}^n}{{nx}^n}+C\mathrm{with}n\ne 0$$

Commented by arcana last updated on 25/May/19

$$\mathrm{thanks}$$

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