Question Number 42579 by Raj Singh last updated on 28/Aug/18 $$\int\:{sinx}/\sqrt{\mathrm{1}+{sinx}} \\ $$ Commented by maxmathsup by imad last updated on 28/Aug/18 $${let}\:{A}\:=\:\int\:\:\:\frac{{sinx}}{\:\sqrt{\mathrm{1}+{sinx}}}\:{dx}\:\:{we}\:{have}\:\:\mathrm{1}+{sinx}\:=\mathrm{1}+\mathrm{2}{sin}\left(\frac{{x}}{\mathrm{2}}\right){cos}\left(\frac{{x}}{\mathrm{2}}\right) \\ $$$$=\left({sin}\left(\frac{{x}}{\mathrm{2}}\right)\:+{cos}\left(\frac{{x}}{\mathrm{2}}\right)\right)^{\mathrm{2}}…
Question Number 108099 by bemath last updated on 14/Aug/20 $$\:\:\:\:\frac{\bigstar\mathcal{B}{e}\mathcal{M}{ath}\circledcirc}{\sqcap} \\ $$$$\:\left(\mathrm{1}\right)\:\int\:{x}\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\:{dx}\:? \\ $$$$\left(\mathrm{2}\right)\:{Find}\:{the}\:{distance}\:{of}\:{the}\:{point}\: \\ $$$$\left(\mathrm{3},\mathrm{3},\mathrm{1}\right)\:{from}\:{the}\:{plane}\:\Pi\:{with}\:{equation} \\ $$$$\left(\overset{\rightarrow} {{r}}−\overset{\rightarrow} {{i}}−\overset{\rightarrow} {{j}}\right)\bullet\left(\overset{\rightarrow} {{i}}−\overset{\rightarrow} {{j}}+\overset{\rightarrow} {{k}}\right)\:=\:\mathrm{0}\:,\:{also}\:…
Question Number 108095 by bemath last updated on 14/Aug/20 $$\:\:\:\frac{\infty\mathcal{B}{e}\mathcal{M}{ath}\infty}{\spadesuit} \\ $$$$\:\:\:\int\:\mathrm{2}{x}\:\mathrm{cos}^{−\mathrm{1}} \left({x}\right)\:{dx}\: \\ $$ Answered by bemath last updated on 14/Aug/20 Answered by Dwaipayan…
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Question Number 108076 by Sarah85 last updated on 14/Aug/20 $$\mathrm{can}\:\mathrm{someone}\:\mathrm{please}\:\mathrm{show}\:\mathrm{how}\:\mathrm{to}\:\mathrm{get} \\ $$$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\mathrm{sin}\:\left({a}\:\mathrm{sin}\:\left({x}\right)\right)\:{dx}=\pi\mathrm{H}_{\mathrm{0}} \:\left({a}\right) \\ $$$$\mathrm{where}\:\mathrm{H}_{\mathrm{0}} \:\left({a}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{Struve}−\mathrm{H}−\mathrm{Function} \\ $$ Terms of Service Privacy Policy…
Question Number 108073 by bemath last updated on 14/Aug/20 $$\:\:\:\:\frac{\triangleq\mathcal{B}{e}\mathcal{M}{ath}\triangleq}{\prec} \\ $$$$\:\:\int\:\frac{{x}\:{dx}}{{x}^{\mathrm{8}} −\mathrm{1}}\:? \\ $$ Answered by john santu last updated on 14/Aug/20 $$\:\:\:\:\frac{\Box\mathcal{JS}\boxdot}{≢} \\…
Question Number 42506 by maxmathsup by imad last updated on 26/Aug/18 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left({t}\right)}{\left(^{\mathrm{3}} \sqrt{{t}^{\mathrm{2}} }\right)\left(\mathrm{1}+{t}\right)}{dt}\:. \\ $$ Commented by maxmathsup by imad last updated…
Question Number 42504 by maxmathsup by imad last updated on 26/Aug/18 $${let}\:{x}>\mathrm{0}\:{prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{e}^{−{t}^{\mathrm{2}} } {ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }\:{dt}\:=\pi\:\int_{\mathrm{0}} ^{\sqrt{{x}}} \:\:{e}^{\frac{\mathrm{1}}{{u}^{\mathrm{2}} }} \:\:{du}\:. \\…
Question Number 42505 by maxmathsup by imad last updated on 26/Aug/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left({t}\right)}{\left(\mathrm{1}+{t}\right)\sqrt{{t}}}\:{dt}\:. \\ $$ Commented by maxmathsup by imad last updated on 29/Aug/18…
Question Number 42503 by maxmathsup by imad last updated on 26/Aug/18 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} } \\ $$ Commented by maxmathsup by imad last updated…
Question Number 42501 by maxmathsup by imad last updated on 26/Aug/18 $${calculate}\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}\left(\mathrm{4}{x}\right)}{{cosx}\:+{sinx}}\:\:{and}\:{J}\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sin}\left(\mathrm{4}{x}\right)}{{cosx}\:+{sinx}}{dx} \\ $$ Commented by maxmathsup by imad last updated…