Question Number 155134 by amin96 last updated on 25/Sep/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \boldsymbol{\mathrm{sin}}^{\mathrm{2}\boldsymbol{\mathrm{n}}} \left({x}\right){dx}=? \\ $$ Answered by phanphuoc last updated on 26/Sep/21 $$\pi/\mathrm{24}^{{n}} .\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}\:\:\:\:\:\:{this}\:{is}\:{wallis}'={intergral} \\…
Question Number 89596 by A8;15: last updated on 18/Apr/20 Commented by john santu last updated on 18/Apr/20 $$\sqrt{\frac{{x}}{\mathrm{1}−{x}}}\:=\:{t}\:\Rightarrow\:{x}\:=\:\frac{{t}^{\mathrm{2}} }{{t}^{\mathrm{2}} +\mathrm{1}} \\ $$$$\left.{dx}\:=\:\frac{\mathrm{2}{t}}{\left({t}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:{dt}\:\right]\: \\…
Question Number 155135 by amin96 last updated on 25/Sep/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\boldsymbol{\mathrm{log}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\right)−\boldsymbol{\mathrm{log}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\right)}{\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{log}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\right)\right)−\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{log}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\right)\right)}\right)^{\mathrm{2}} \boldsymbol{\mathrm{dxdy}}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89593 by M±th+et£s last updated on 19/Apr/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({sec}\left({x}\right)\right)\:{ln}\left({csc}\left({x}\right)\right)\:{dx}=\frac{\pi^{\mathrm{2}} \:{ln}^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{2}}−\frac{\pi^{\mathrm{4}} }{\mathrm{48}} \\ $$ Commented by maths mind last updated…
Question Number 89584 by jagoll last updated on 18/Apr/20 $$\int\:\frac{\mathrm{sin}\:^{\mathrm{4}} \left(\mathrm{x}\right)\:\mathrm{dx}}{\mathrm{4}+\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{x}\right)} \\ $$ Commented by mathmax by abdo last updated on 18/Apr/20 $${I}\:=\int\:\:\frac{{sin}^{\mathrm{4}} {xdx}}{\mathrm{4}+{cos}^{\mathrm{2}}…
Question Number 155058 by HarshSahu last updated on 24/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 23972 by Sudipta Jana last updated on 10/Nov/17 $$\int_{\mathrm{0}} ^{\mathrm{90}} \frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{sin}\:^{\mathrm{4}} {x}+\mathrm{cos}\:^{\mathrm{4}} {x}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89511 by M±th+et£s last updated on 17/Apr/20 $$\int_{\mathrm{0}} ^{\mathrm{3}\pi} \sqrt{\mathrm{1}+{sin}^{\mathrm{4}} \frac{\theta}{\mathrm{3}}\:{cos}^{\mathrm{2}} \frac{\theta}{\mathrm{3}}}\:{d}\theta \\ $$ Commented by mr W last updated on 17/Apr/20 $${please}\:{go}\:{to}\:{Q}\mathrm{89482}\:{and}\:{report}\:{that}…
Question Number 89489 by cindiaulia last updated on 17/Apr/20 $$\int_{−\mathrm{1}} ^{\mathrm{4}} \mathrm{x}\sqrt{×+\mathrm{5}\:}\mathrm{dx} \\ $$ Commented by M±th+et£s last updated on 17/Apr/20 $${let}\:{x}+\mathrm{5}={u}\:\:{x}={u}−\mathrm{5}\:\:\:\:{du}={dx} \\ $$$$\int_{−\mathrm{1}} ^{\mathrm{4}}…
Question Number 89487 by cindiaulia last updated on 17/Apr/20 $$\int_{−\mathrm{1}} ^{\mathrm{3}} \frac{\mathrm{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{x}+\mathrm{2}}}\:\mathrm{dx} \\ $$ Commented by niroj last updated on 17/Apr/20 $$\:\int_{−\mathrm{1}} ^{\:\mathrm{3}} \:\frac{\:\mathrm{x}^{\mathrm{2}}…