Question Number 157309 by cortano last updated on 22/Oct/21 $$\:\:\int\:\frac{{dx}}{\:\sqrt{{x}}+{x}\sqrt{{x}+\mathrm{1}}}\:=? \\ $$ Answered by MJS_new last updated on 22/Oct/21 $$\int\frac{{dx}}{\:\sqrt{{x}}+{x}\sqrt{{x}+\mathrm{1}}}= \\ $$$$=\int\frac{\sqrt{{x}+\mathrm{1}}}{{x}^{\mathrm{2}} +{x}−\mathrm{1}}{dx}−\int\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}−\mathrm{1}\right)\sqrt{{x}}} \\…
Question Number 91774 by frc2crc last updated on 03/May/20 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:^{{k}} \left({x}\right)}{{x}^{{k}} }{dx}\:{for}\:{any}\:{k}>\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 91771 by M±th+et+s last updated on 03/May/20 $$\int_{\mathrm{0}} ^{\infty} \frac{{sin}^{\mathrm{3}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$ Commented by abdomathmax last updated on 03/May/20 $${let}\:{I}=\int_{\mathrm{0}} ^{\infty}…
Question Number 91753 by Rio Michael last updated on 02/May/20 $$\int\mathrm{3}\:\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} \:{dx}\:=\:?? \\ $$ Commented by peter frank last updated on 02/May/20 $${by}\:{part} \\ $$…
Question Number 157268 by gsk2684 last updated on 21/Oct/21 $${prove}\:{that} \\ $$$$\int\frac{{x}^{\mathrm{2}} }{\left({x}\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} }{dx}=−\frac{{x}\mathrm{sec}\:{x}}{{x}\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}+\mathrm{tan}\:{x}+{c} \\ $$ Answered by Ar Brandon last updated on 18/Nov/21 $${I}=\int\frac{{x}^{\mathrm{2}}…
Question Number 91735 by frc2crc last updated on 02/May/20 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \sqrt[{{k}}]{\mathrm{tan}^{{m}} \:\alpha}\:{d}\alpha\:{for}\:{m}>\mathrm{1} \\ $$ Commented by mathmax by abdo last updated on 03/May/20 $${I}\:=\int_{\mathrm{0}}…
Question Number 157257 by john_santu last updated on 21/Oct/21 $$\int\:\frac{\mathrm{sin}\:^{\mathrm{6}} {x}+\mathrm{cos}\:^{\mathrm{5}} {x}}{\mathrm{sin}\:^{\mathrm{2}} {x}\:\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx} \\ $$ Answered by qaz last updated on 21/Oct/21 $$\int\frac{\mathrm{sin}\:^{\mathrm{6}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{5}}…
Question Number 91714 by jagoll last updated on 02/May/20 Commented by Tony Lin last updated on 02/May/20 $$\int_{\mathrm{0}} ^{\mathrm{2}} \left({ln}\mathrm{3}^{\frac{\mathrm{2}\pi}{\mathrm{3}}} \right){e}^{{x}^{\mathrm{2}} } {dx} \\ $$$$=\left({ln}\mathrm{3}^{\frac{\mathrm{2}\pi}{\mathrm{3}}}…
Question Number 157254 by physicstutes last updated on 21/Oct/21 $$\mathrm{Show}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx}\:=\:\mathrm{ln}\left(\frac{\mathrm{4}}{\mathrm{3}}\right) \\ $$ Answered by puissant last updated on 21/Oct/21 $$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 157251 by mnjuly1970 last updated on 21/Oct/21 $$ \\ $$$$\:\:\:\:\:#\:\mathrm{Nice}\:\mathrm{Mathematics}\:# \\ $$$$\:\:\:\:\:\:\:…{calculation}\:… \\ $$$$\:\:\:\:\:\:\:\:\Omega\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{tanh}^{\:−\mathrm{1}} \:\left(\sqrt{\:{x}}\:\right)}{{x}}\:{dx}\:\overset{?} {=}\:\frac{\:\pi^{\:\mathrm{2}} }{\mathrm{4}} \\ $$$$\:\:\:−−−−−−−−−−−−− \\ $$$$\:\:\:\:\Omega\::\overset{\sqrt{{x}}\:=\:{t}}…