Question Number 143098 by mnjuly1970 last updated on 10/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{Prove}….\: \\ $$$$\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{s}{inh}\left(\pi{n}\right)}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{6}}\:−\frac{\mathrm{1}}{\mathrm{2}\pi}\:\:\:… \\ $$$$\:\:\:\:\:\:\:…… \\ $$ Answered by Dwaipayan Shikari…
Question Number 143094 by bramlexs22 last updated on 10/Jun/21 Answered by liberty last updated on 10/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 77552 by lémùst last updated on 07/Jan/20 $$\int\frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx}\:=\:? \\ $$ Answered by MJS last updated on 07/Jan/20 $$\int\frac{{x}−\mathrm{2}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}−\mathrm{4}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}{dx}= \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}−\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 143087 by bramlexs22 last updated on 10/Jun/21 Answered by Ar Brandon last updated on 10/Jun/21 $$\mathrm{x}=\mathrm{sec}\vartheta \\ $$$$\mathrm{I}=\int_{\frac{\mathrm{2}\pi}{\mathrm{3}}} ^{\frac{\mathrm{5}\pi}{\mathrm{6}}} \frac{\mathrm{sec}\vartheta\mathrm{tan}\vartheta}{\mathrm{sec}\vartheta\sqrt{\mathrm{sec}^{\mathrm{2}} \vartheta−\mathrm{1}}}\mathrm{d}\vartheta=\int_{\frac{\mathrm{2}\pi}{\mathrm{3}}} ^{\frac{\mathrm{5}\pi}{\mathrm{6}}} \frac{\mathrm{tan}\vartheta}{\:\sqrt{\mathrm{tan}^{\mathrm{2}}…
Question Number 77549 by BK last updated on 07/Jan/20 Commented by abdomathmax last updated on 08/Jan/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dz}}{\mathrm{1}−{xyz}}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\sum_{{n}=\mathrm{0}} ^{\infty} {x}^{{n}} {y}^{{n}} \:{z}^{{n}}…
Question Number 143080 by Mathspace last updated on 09/Jun/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Answered by qaz last updated on 10/Jun/21 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 143081 by Mathspace last updated on 09/Jun/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} {xe}^{−{x}^{\mathrm{2}} } {arctanx}\:{dx} \\ $$ Answered by qaz last updated on 10/Jun/21 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 143082 by Mathspace last updated on 09/Jun/21 $${calculate}\:{f}\left({a},{b}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{ax}^{\mathrm{2}} } }{{x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} }{dx} \\ $$$${with}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$ Answered by Dwaipayan Shikari last…
Question Number 143083 by Mathspace last updated on 09/Jun/21 $${calculate}\:\Psi\left({a},{b}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{ax}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$$${with}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$ Answered by Olaf_Thorendsen last…
Question Number 77536 by ~blr237~ last updated on 07/Jan/20 $$\mathrm{find}\:\mathrm{all}\:\mathrm{function}\:\mathrm{that}\:\mathrm{satisfy} \\ $$$$\:\:\forall\:\mathrm{p}>\mathrm{0}\:\:\:\int_{\mathrm{0}} ^{\infty} \mathrm{f}\left(\mathrm{t}\right)\mathrm{e}^{−\mathrm{pt}} \mathrm{dt}=\:\mathrm{e}^{−\mathrm{pT}} \:\:\:\:\:\:\mathrm{with}\:\mathrm{T}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{real} \\ $$ Answered by JDamian last updated on 07/Jan/20…