Question Number 133291 by liberty last updated on 21/Feb/21 $$\:\int\:\frac{\left(\mathrm{x}^{\mathrm{4}} \right)^{\mathrm{2}} }{\left(\mathrm{1}+\mathrm{x}^{\mathrm{6}} \right)^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$ Answered by EDWIN88 last updated on 21/Feb/21 $$\mathrm{integration}\:\mathrm{by}\:\mathrm{parts} \\…
Question Number 2210 by Yozzi last updated on 08/Nov/15 $${Evaluate}\: \\ $$$$\:\:\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{2}} {cos}\alpha+\mathrm{1}}\:\:\left(\mathrm{0}<\alpha<\pi\right). \\ $$ Commented by 123456 last updated on 09/Nov/15…
Question Number 67744 by mathmax by abdo last updated on 31/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({t}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({t}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}}…
Question Number 133268 by mnjuly1970 last updated on 20/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:….{calculus}… \\ $$$$\:\:{prove}:: \\ $$$$\:\:\:\boldsymbol{\phi}=\int_{−\infty} ^{\:+\infty} \frac{{dx}}{\left({x}^{\mathrm{2}} +\pi^{\mathrm{2}} \right){cosh}\left({x}\right)}=\frac{\mathrm{4}}{\boldsymbol{\pi}}\:−\mathrm{1} \\ $$$$ \\ $$ Answered by Ajetunmobi…
Question Number 2186 by Yozzi last updated on 07/Nov/15 $${Let}\:{J}=\int_{\mathrm{0}} ^{\infty} {f}\left(\left({x}−{x}^{−\mathrm{1}} \right)^{\mathrm{2}} \right){dx}\:{where}\:{f}\:{is} \\ $$$${any}\:{function}\:{for}\:{which}\:{the}\:{integral} \\ $$$${exists}.\:{Show}\:{that} \\ $$$${J}=\int_{\mathrm{0}} ^{\infty} {x}^{−\mathrm{2}} {f}\left(\left({x}−{x}^{−\mathrm{1}} \right)^{\mathrm{2}} \right){dx}=\mathrm{0}.\mathrm{5}\int_{\mathrm{0}}…
Question Number 2176 by Filup last updated on 06/Nov/15 $$\mathrm{Is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{integrate}\:\mathrm{the}\:\mathrm{following}: \\ $$$$ \\ $$$$\int\mathrm{sin}\left(\mathrm{cos}\:\theta\right){d}\theta \\ $$ Commented by 123456 last updated on 07/Nov/15 $$\mathrm{i}\:\mathrm{dont}\:\mathrm{know}\:\mathrm{if}\:\mathrm{it}\:\mathrm{help}\:\mathrm{but} \\…
Question Number 67708 by aliesam last updated on 30/Aug/19 Answered by mind is power last updated on 30/Aug/19 $${z}=\frac{{x}}{{y}} \\ $$$${y}=\frac{{x}}{{z}} \\ $$$${dy}=−\frac{{x}}{{z}^{\mathrm{2}} }{dz} \\…
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Question Number 67696 by mhmd last updated on 30/Aug/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}\right)/\left(\mathrm{1}+{x}\right){lnx}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 133228 by mnjuly1970 last updated on 20/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{advanced}\:\:\:\:{calculus}…. \\ $$$$\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\Gamma\left({n}+\frac{\mathrm{1}}{\mathrm{2}}\right)\psi\left({n}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{\mathrm{2}^{{n}} .{n}!}=−\sqrt{\mathrm{2}\pi}\:\left(\gamma+{ln}\left(\mathrm{2}\right)\right)…. \\ $$$$ \\ $$ Answered by Dwaipayan Shikari…