Question Number 207723 by SANOGO last updated on 24/May/24
$$\mathrm{li}{m}\int_{\mathrm{0}} ^{\infty} \left(\mathrm{1}−{e}^{−{ncos}\left({x}\right)} \right){dx} \\ $$
Commented by Frix last updated on 24/May/24
$${f}\left({x}\right)=\mathrm{1}−\mathrm{e}^{−{n}\mathrm{cos}\:{x}} \\ $$$${n}\rightarrow\infty\:\Rightarrow\:{f}\left({x}\right)=\begin{cases}{\mathrm{1};\:−\frac{\pi}{\mathrm{2}}+{k}\pi\leqslant{x}\leqslant\frac{\pi}{\mathrm{2}}+{k}\pi}\\{−\infty;\:\frac{\pi}{\mathrm{2}}+{k}\pi<{x}<\frac{\mathrm{3}\pi}{\mathrm{2}}+{k}\pi}\end{cases}\forall{k}\in\mathbb{Z} \\ $$$$\mathrm{This}\:\mathrm{integral}\:\mathrm{cannot}\:\mathrm{converge}. \\ $$
Commented by SANOGO last updated on 25/May/24
$${thank}\:{you} \\ $$