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calculate-lim-x-pi-pi-x-x-2-pi-t-e-t-2-x-pi-x-2-pi-t-2-lnt-dt-




Question Number 167004 by qaz last updated on 04/Mar/22
calculate ::  lim_(x→(√π)) ∫_(√π) ^x (((x^2 +(√π)t)e^t^2  )/((x−(√π))(x^2 +π)t^2 lnt))dt=?
$$\mathrm{calculate}\:::\:\:\underset{\mathrm{x}\rightarrow\sqrt{\pi}} {\mathrm{lim}}\int_{\sqrt{\pi}} ^{\mathrm{x}} \frac{\left(\mathrm{x}^{\mathrm{2}} +\sqrt{\pi}\mathrm{t}\right)\mathrm{e}^{\mathrm{t}^{\mathrm{2}} } }{\left(\mathrm{x}−\sqrt{\pi}\right)\left(\mathrm{x}^{\mathrm{2}} +\pi\right)\mathrm{t}^{\mathrm{2}} \mathrm{lnt}}\mathrm{dt}=? \\ $$

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