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Question Number 126183 by bobhans last updated on 18/Dec/20

$${\int }_0^{\mathrm{\infty }}\frac{e^{2\pi x}-1}{e^{2\pi x}+1}(\frac{1}{x}-\frac{1}{N^2+x^2})dx$$

Answered by Olaf last updated on 19/Dec/20

$$\mathrm{\Omega }={\int }_0^{\mathrm{\infty }}\tanh \left(\pi x\right)[\frac{1}{x}-\frac{1}{{\mathrm{N}}^2+x^2}]dx$$$$\mathrm{but}\tanh \left(\pi x\right)[\frac{1}{x}-\frac{1}{{\mathrm{N}}^2+x^2}]\underset{\mathrm{\infty }}{\sim }\frac{1}{x}-\frac{1}{{\mathrm{N}}^2+x^2}$$$$\mathrm{and}{\int }_0^{\mathrm{\infty }}(\frac{1}{x}-\frac{1}{{\mathrm{N}}^2+x^2})dx\mathrm{diverges}$$$$\mathrm{so}\mathrm{I}\mathrm{suppose}\mathrm{\Omega }\mathrm{diverges}...$$

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