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Prove-lim-x-xe-x-1-x-e-t-sin-t-t-dt-1-2-




Question Number 159935 by qaz last updated on 22/Nov/21
Prove::    lim_(x→+∞) ^(−) xe^(−x) ∫_1 ^x ((e^t sin t)/t)dt=(1/( (√2)))
$$\mathrm{Prove}::\:\:\:\:\underset{\mathrm{x}\rightarrow+\infty} {\overline {\mathrm{lim}}xe}^{−\mathrm{x}} \int_{\mathrm{1}} ^{\mathrm{x}} \frac{\mathrm{e}^{\mathrm{t}} \mathrm{sin}\:\mathrm{t}}{\mathrm{t}}\mathrm{dt}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$

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