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prove-that-x-2-e-x-2-cos-x-2-sin-x-2-dx-pi-sin-3-2-tan-1-2-4-125-1-4-anyone-can-help-me-with-this-please-

Question Number 60611 by aliesam last updated on 22/May/19 $${prove}\:{that}\:\underset{−\infty} {\overset{\infty} {\int}}{x}^{\mathrm{2}} {e}^{−{x}^{\mathrm{2}} } {cos}\left({x}^{\mathrm{2}} \right){sin}\left({x}^{\mathrm{2}} \right)\:{dx}\:=\:\frac{\sqrt{\pi}{sin}\left(\frac{\mathrm{3}}{\mathrm{2}}{tan}^{−\mathrm{1}} \left(\mathrm{2}\right)\right)}{\mathrm{4}\:\sqrt[{\mathrm{4}}]{\mathrm{125}}} \\ $$$${anyone}\:{can}\:{help}\:{me}\:{with}\:{this}\:{please} \\ $$$$ \\ $$ Answered…

x-1-x-2-3-dx-

Question Number 191668 by SEKRET last updated on 28/Apr/23 $$\:\:\:\:\int\:\:\frac{\sqrt{\boldsymbol{\mathrm{x}}}}{\:\sqrt{\left(\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)^{\mathrm{3}} }}\boldsymbol{\mathrm{dx}}\:\:\:\:=\:\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Prove-that-2-n-2-gt-n-2-for-n-N-by-mathematical-induction-

Question Number 126124 by ZiYangLee last updated on 17/Dec/20 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{2}^{{n}} +\mathrm{2}>{n}^{\mathrm{2}\:} \mathrm{for}\:{n}\in\mathbb{N}\:\mathrm{by} \\ $$$$\mathrm{mathematical}\:\mathrm{induction}. \\ $$ Commented by talminator2856791 last updated on 17/Dec/20 $$\:\mathrm{i}\:\mathrm{was}\:\mathrm{having}\:\mathrm{the}\:\mathrm{time}\:\mathrm{of}\:\mathrm{my}\:\mathrm{life}\:\mathrm{till}\:\mathrm{i}\:\mathrm{read}\:“\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}''! \\…