Question Number 190937 by Spillover last updated on 14/Apr/23 $$\mathrm{Show}\:\:\mathrm{that}\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\mathrm{sech}\:\sqrt{\mathrm{x}}\:\mathrm{tanh}\:\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{x}}}=−\frac{\mathrm{2}}{\mathrm{cosh}\:\sqrt{\mathrm{x}}} \\ $$ Answered by ARUNG_Brandon_MBU last updated on 15/Apr/23 $${I}=\int\frac{\left(\mathrm{sech}\sqrt{{x}}\right)\left(\mathrm{tanh}\sqrt{{x}}\right)}{\:\sqrt{{x}}}{dx}=\int\frac{\mathrm{sinh}\sqrt{{x}}}{\:\sqrt{{x}}\mathrm{cosh}^{\mathrm{2}} \sqrt{{x}}}{dx} \\ $$$${t}=\mathrm{cosh}\sqrt{{x}}\:\Rightarrow{dt}=\frac{\mathrm{sinh}\sqrt{{x}}}{\mathrm{2}\sqrt{{x}}}{dx}…
Question Number 125390 by mnjuly1970 last updated on 10/Dec/20 $$\:\:\:\:\:\:\:\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{evaluate}\:::::\curvearrowright \\ $$$$\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{\sqrt{{x}}\:{tan}^{−\mathrm{1}} \left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=??? \\ $$ Answered by mathmax by abdo…
Question Number 125381 by liberty last updated on 10/Dec/20 $$\:{F}\left({x}\right)\:=\:\mathrm{cos}\:\left(\underset{\mathrm{1}} {\overset{{x}} {\int}}\:\mathrm{cos}\:\left(\underset{\mathrm{1}} {\overset{{t}} {\int}}\:\mathrm{sin}\:^{\mathrm{3}} {u}\:{du}\:\right){dy}\right) \\ $$$$\:\frac{{dF}\left({x}\right)}{{dx}}\:=\:?\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 59846 by bhanukumarb2@gmail.com last updated on 15/May/19 Commented by MJS last updated on 15/May/19 $$\mathrm{do}\:\mathrm{you}\:\mathrm{have}\:\mathrm{an}\:\mathrm{answer}? \\ $$$$\mathrm{it}\:\mathrm{seems}\:\mathrm{to}\:\mathrm{be}\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Commented by bhanukumarb2@gmail.com last…
Question Number 59834 by bhanukumarb2@gmail.com last updated on 15/May/19 Answered by tanmay last updated on 15/May/19 $$\mathrm{1}>{sin}\left(\mathrm{3}{x}\right)>−\mathrm{1} \\ $$$$\:\left({x}−\mathrm{1}\right)\geqslant{x}+{sin}\left(\mathrm{3}{x}\right)\geqslant{x}−\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\pi} {sin}^{\mathrm{4}} \left({x}+\mathrm{1}\right){dx}\geqslant\int_{\mathrm{0}} ^{\pi}…
Question Number 59825 by aliesam last updated on 15/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 125346 by john_santu last updated on 10/Dec/20 $$\:\int\:{x}\:\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }\:{dx}?? \\ $$ Commented by AdeyemiAdebola last updated on 10/Dec/20 $${e}^{{ix}} =\:{cosx}\:+\:{isinx} \\ $$ Answered…
Question Number 59807 by aliesam last updated on 15/May/19 $$\int\frac{{x}−\mathrm{1}}{\:\sqrt{\mathrm{2}{x}−{x}^{\mathrm{2}} }}\:{dx} \\ $$ Answered by tanmay last updated on 15/May/19 $${t}^{\mathrm{2}} =\mathrm{2}{x}−{x}^{\mathrm{2}} \\ $$$$\mathrm{2}{tdt}=\left(\mathrm{2}−\mathrm{2}{x}\right){dx} \\…
Question Number 59803 by bhanukumarb2@gmail.com last updated on 15/May/19 Commented by maxmathsup by imad last updated on 16/May/19 $${let}\:{A}\:=\frac{\mathrm{1}}{\pi^{\mathrm{2}} }\:\int_{\mathrm{0}} ^{\infty} \:\frac{\left({lnx}\right)^{\mathrm{2}} }{\:\sqrt{{x}}\left(\mathrm{1}−{x}\right)^{\mathrm{2}} }\:{dx}\:\Rightarrow\pi^{\mathrm{2}} \:{A}\:=_{\sqrt{{x}}={t}}…
Question Number 59802 by bhanukumarb2@gmail.com last updated on 15/May/19 Commented by bhanukumarb2@gmail.com last updated on 15/May/19 $${please}\:{solve}\:{the}\:{problems}\: \\ $$ Terms of Service Privacy Policy Contact:…