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Question Number 126904 by Mustafa2020 last updated on 25/Dec/20

$${\int }_0^{\mathrm{\infty }}\frac{x}{1+x^2{sin}^{2}x}dx$$

Answered by mindispower last updated on 25/Dec/20

$$⩾\mathrm{\Sigma }{\int }_{2k\pi }^{2k\pi +\frac{\pi }{6}}\frac{x}{1+x^2{sin}^2\left(x\right)}dx⩾\sum _{k⩾0}\frac{\left(2k\pi \right)}{1+{(2k\pi +\frac{\pi }{6})}^2.\frac{1}{4}}$$$$wichdiverge\sim \frac{1}{2\pi k}harmonicserie$$$$$$

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