Question Number 79627 by mathmax by abdo last updated on 26/Jan/20 $$\left.\mathrm{1}\right)\:{expicite}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{with}\:{x}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 79615 by M±th+et£s last updated on 26/Jan/20 $${prove}\:{that}\:{with}\:{using}\:{hypergeometric}\:{function} \\ $$$$\int_{\mathrm{0}} ^{\pi} {sin}\left({x}^{\mathrm{2}} \right)=\frac{\pi^{\mathrm{3}} }{\mathrm{3}}\:\mathrm{1}{F}_{\mathrm{2}} \left[\frac{\mathrm{3}}{\mathrm{4}};\frac{\mathrm{3}}{\mathrm{2}};\frac{\mathrm{7}}{\mathrm{4}};\frac{−\pi^{\mathrm{4}} }{\mathrm{4}}\right]\: \\ $$ Commented by mind is power…
Question Number 79612 by john santu last updated on 26/Jan/20 $$\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}\:}\left(\sqrt[{\mathrm{4}\:}]{\mathrm{x}}+\mathrm{1}\right)^{\mathrm{10}} }\:=\:? \\ $$ Answered by MJS last updated on 26/Jan/20 $$\int\frac{{dx}}{{x}^{\frac{\mathrm{1}}{\mathrm{2}}} \left({x}^{\frac{\mathrm{1}}{\mathrm{4}}} +\mathrm{1}\right)^{\mathrm{10}} }=…
Question Number 79607 by sou99 last updated on 26/Jan/20 $${Solve}\:{this} \\ $$$$\int_{} \frac{\left({x}−{yz}\right)}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{xyz}\right)^{\mathrm{3}/\mathrm{2}} }{dz} \\ $$$$ \\ $$$$ \\ $$ Commented by MJS…
Question Number 79580 by john santu last updated on 26/Jan/20 $$\mathrm{does}\:\mathrm{this}\:\mathrm{matter}\:\mathrm{reasonable} \\ $$$$\int\:\mathrm{sin}\:^{\mathrm{x}} \left(\mathrm{x}\right)\:\mathrm{dx}\:? \\ $$ Commented by MJS last updated on 26/Jan/20 $$\mathrm{first}\:\mathrm{of}\:\mathrm{all},\:\mathrm{find}\:\mathrm{out}\:\mathrm{where}\:\mathrm{sin}^{{x}} \:{x}\:\mathrm{is}\:\mathrm{defined}……
Question Number 14014 by tawa tawa last updated on 26/May/17 $$\int\mathrm{cos}^{\mathrm{n}} \left(\mathrm{x}\right)\:\:\mathrm{dx} \\ $$$$\mathrm{please}\:\mathrm{i}\:\mathrm{need}\:\mathrm{workings}. \\ $$ Answered by mrW1 last updated on 26/May/17 $${I}_{{n}} =\int\mathrm{cos}^{\mathrm{n}}…
Question Number 145081 by qaz last updated on 02/Jul/21 $$\int_{\mathrm{0}} ^{\infty} \left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{2}}+\frac{\mathrm{x}^{\mathrm{5}} }{\mathrm{2}\centerdot\mathrm{4}}−\frac{\mathrm{x}^{\mathrm{7}} }{\mathrm{2}\centerdot\mathrm{4}\centerdot\mathrm{6}}+…\right)\centerdot\left(\mathrm{1}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{4}^{\mathrm{2}} }+\frac{\mathrm{x}^{\mathrm{6}} }{\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{4}^{\mathrm{2}} \centerdot\mathrm{6}^{\mathrm{2}} }+…\right)\mathrm{dx}=\sqrt{\mathrm{e}} \\…
Question Number 79531 by jagoll last updated on 26/Jan/20 $$\underset{\mathrm{0}} {\int}^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx}\:? \\ $$ Commented by john santu last updated on 26/Jan/20 $${remember}\:\underset{\mathrm{0}} {\overset{\infty}…
Question Number 145064 by akolade last updated on 02/Jul/21 $$\:\:\:\:\:\:\int\mathrm{cos}\:\mathrm{2xln}\:\left(\mathrm{1}+\mathrm{tan}\:\mathrm{x}\right)\mathrm{dx} \\ $$$$\:\:\:\:\:\: \\ $$ Answered by mathmax by abdo last updated on 02/Jul/21 $$\Psi=\int\:\mathrm{cos}\left(\mathrm{2x}\right)\mathrm{log}\left(\mathrm{1}+\mathrm{tanx}\right)\mathrm{dx}\:\:\:\mathrm{by}\:\mathrm{parts} \\…
Question Number 79528 by mathmax by abdo last updated on 25/Jan/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}^{\mathrm{3}} } {cos}\left({x}^{\mathrm{2}} \right){dx} \\ $$ Terms of Service Privacy Policy Contact:…