Question Number 121611 by benjo_mathlover last updated on 10/Nov/20 $$\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\:\mathrm{sin}\:\left(\mathrm{2}\pi\mathrm{x}\right)\mathrm{cos}\:\left(\mathrm{5}\pi\mathrm{x}\right)\:\mathrm{dx}\:?\: \\ $$ Commented by mr W last updated on 10/Nov/20 $$\int_{\mathrm{0}} ^{\mathrm{2}} \mathrm{sin}\:\left(\mathrm{2}\pi{x}\right)\mathrm{cos}\:\left(\mathrm{5}\pi{x}\right){dx}…
Question Number 121602 by benjo_mathlover last updated on 09/Nov/20 Answered by liberty last updated on 10/Nov/20 $$\mathrm{I}=\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{dx}}{\mathrm{b}^{\mathrm{2}} \:\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}+\mathrm{1}} \\ $$$$\mathrm{let}\:\phi=\mathrm{b}\:\mathrm{tan}\:\mathrm{x}\:\Rightarrow\mathrm{d}\phi=\mathrm{bsec}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}\: \\…
Question Number 121601 by benjo_mathlover last updated on 09/Nov/20 $$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{x}\:\sqrt{\mathrm{3}+\mathrm{x}^{\mathrm{2}} }}\:? \\ $$ Answered by liberty last updated on 10/Nov/20 $$\mathrm{let}\:\mathrm{x}\:=\:\sqrt{\mathrm{3}}\:\mathrm{tan}\:\gamma\: \\ $$$$\mathrm{I}=\:\int\:\frac{\sqrt{\mathrm{3}}\:\mathrm{sec}\:^{\mathrm{2}} \gamma}{\:\sqrt{\mathrm{3}}\:\mathrm{tan}\:\gamma\:\sqrt{\mathrm{3}+\mathrm{3tan}\:^{\mathrm{2}} \gamma}}\:\mathrm{d}\gamma…
Question Number 187135 by cortano12 last updated on 14/Feb/23 $$\:\underset{\:\:\mathrm{0}} {\overset{\:\:\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{tan}\:^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx}\:=? \\ $$ Answered by horsebrand11 last updated on 14/Feb/23 $$\:{I}=\underset{\:\mathrm{0}} {\overset{\:\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{tan}\:^{\mathrm{2}}…
Question Number 56060 by necx1 last updated on 09/Mar/19 $$\int{e}^{−{x}^{\mathrm{2}} } {dx}\:{as}\:{an}\:{infinite}\:{series}.{Hence} \\ $$$${investigate}\:{its}\:{converge}. \\ $$ Commented by maxmathsup by imad last updated on 09/Mar/19…
Question Number 56061 by necx1 last updated on 09/Mar/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{−{x}^{\mathrm{2}} } {dx}\:{correct}\:{to}\:\mathrm{3}\:{decimal}\:{place}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 09/Mar/19 $$\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 187095 by normans last updated on 13/Feb/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:−\:\boldsymbol{{x}}^{\mathrm{2}} }}\:\:+\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}\:−\:\boldsymbol{{x}}^{\mathrm{2}} }}\:\:\boldsymbol{{dx}}\:\:\:\:\:\: \\ $$$$ \\ $$ Commented by Frix last updated…
Question Number 121548 by benjo_mathlover last updated on 09/Nov/20 $$\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\mathrm{tan}\:^{\mathrm{6}} \mathrm{x}\:\mathrm{sec}\:\mathrm{x}\:\mathrm{dx}\:=? \\ $$ Answered by MJS_new last updated on 09/Nov/20 $$\int\mathrm{tan}^{\mathrm{6}} \:{x}\:\mathrm{sec}\:{x}\:{dx}=\int\frac{\mathrm{sin}^{\mathrm{6}} \:{x}}{\mathrm{cos}^{\mathrm{7}}…
Question Number 55998 by maxmathsup by imad last updated on 07/Mar/19 $${find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {arctan}\left({t}^{\mathrm{2}} +{xt}\:+\mathrm{1}\right){dt}\:\:. \\ $$ Commented by MJS last updated on 08/Mar/19 $$\mathrm{we}\:\mathrm{can}\:\mathrm{use}\:\mathrm{my}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{55994}\:\mathrm{but}\:\mathrm{it}'\mathrm{s}…
Question Number 55999 by Easyman32 last updated on 07/Mar/19 Commented by tanmay.chaudhury50@gmail.com last updated on 08/Mar/19 $${still}\:{to}\:{find}\:{the}\:{way}\:{to}\:{start}… \\ $$ Terms of Service Privacy Policy Contact:…