Menu Close

Category: Integration

1-expicite-f-x-0-1-ln-1-xt-2-1-t-2-dt-with-x-0-2-calculate-0-1-ln-1-t-2-1-t-2-dt-and-0-1-ln-1-2t-2-1-t-2-dt-

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}}…

prove-that-with-using-hypergeometric-function-0-pi-sin-x-2-pi-3-3-1F-2-3-4-3-2-7-4-pi-4-4-

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…

dx-x-x-1-4-1-10-

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}} }=…

does-this-matter-reasonable-sin-x-x-dx-

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}……

0-x-x-3-2-x-5-2-4-x-7-2-4-6-1-x-2-2-2-x-4-2-2-4-2-x-6-2-2-4-2-6-2-dx-e-

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}} \\…

1-0-ln-1-x-x-x-2-1-dx-

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}…

cos-2xln-1-tan-x-dx-

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} \\…