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Question Number 141933 by mathmax by abdo last updated on 24/May/21

$$\mathrm{let}\mathrm{f}\left(\mathrm{t}\right)={\int }_0^{\mathrm{\infty }}\frac{\mathrm{logx}}{{\mathrm{x}}^2+{\mathrm{t}}^2}\mathrm{dx}(\mathrm{t}>0)$$ $$1)\mathrm{calculate}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(\mathrm{t}\right)\mathrm{and}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(0\right)$$ $$2)\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{integr}\mathrm{serie}$$

Commented byMathspace last updated on 24/May/21

$$f^{\left(n\right)}\left(1\right)$$

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