Question Number 86288 by john santu last updated on 28/Mar/20 $$\int\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{4}} \right)^{\mathrm{1}/\mathrm{4}} } \\ $$ Answered by TANMAY PANACEA. last updated on 28/Mar/20 $${x}^{\mathrm{2}} ={tana}…
Question Number 151819 by mnjuly1970 last updated on 23/Aug/21 $$ \\ $$$$\:\:\:\:\:\mathrm{1}.\:{prove}\:{that}\:: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \frac{\:{e}^{\:{t}} .{ln}\left({t}\:\right)}{\left(\mathrm{1}\:+\:{e}^{\:{t}} \right)^{\:\mathrm{2}} }\:{dt}=\frac{\mathrm{1}}{\mathrm{2}}\left({ln}\left(\frac{\pi}{\mathrm{2}}\:\right)−\:\gamma\:\right)\: \\ $$$$\:\:\: \\ $$ Answered by…
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Question Number 86242 by niroj last updated on 27/Mar/20 $$\:\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{C}}\mathrm{F}+\boldsymbol{\mathrm{P}}\mathrm{I}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }+\mathrm{3}\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}+\mathrm{2}\boldsymbol{\mathrm{y}}=\:\boldsymbol{\mathrm{e}}^{\mathrm{2}\boldsymbol{\mathrm{x}}} \:\boldsymbol{\mathrm{sinx}}\:. \\ $$$$\: \\ $$$$ \\ $$ Answered by TANMAY PANACEA.…
Question Number 151744 by mnjuly1970 last updated on 22/Aug/21 $$ \\ $$$$\:\:\:\:\:\:\:\:{show}\:\:{that}…. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathscr{F}\::=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}^{\:\mathrm{4}} \:\left({x}^{\:\mathrm{2}} \:\right)\:}{{x}^{\:\mathrm{2}} }\:{dx}\:=\:\frac{\mathrm{1}}{\mathrm{8}}\:\left(\:\mathrm{4}\:−\:\sqrt{\mathrm{2}}\:\right)\sqrt{\pi}\:…..\blacksquare\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:…{m}.{n}… \\ $$$$…
Question Number 151685 by iloveisrael last updated on 22/Aug/21 $$\:\:{Find}\:{maximum}\:{value}\:{of}\:{function} \\ $$$$\:\:\alpha\left({x}\right)=\:\sqrt{\mathrm{2}{x}}\:+\sqrt{\mathrm{16}−{x}}\:+\sqrt{\mathrm{35}+{x}}\:. \\ $$ Answered by mr W last updated on 22/Aug/21 $${x}\geqslant\mathrm{0} \\ $$$${x}\leqslant\mathrm{16}…
Question Number 86092 by ar247 last updated on 27/Mar/20 $$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}−\mathrm{4}{x}−\mathrm{2}{x}^{\mathrm{2}} }}{dx} \\ $$ Commented by abdomathmax last updated on 27/Mar/20 $${I}\:=\int\:\:\frac{{dx}}{\:\sqrt{−\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}}}\:\:{we}\:{have} \\ $$$${I}=\int\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{5}−\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}−\mathrm{1}\right)}}=\int\:\:\frac{{dx}}{\:\sqrt{\mathrm{5}−\mathrm{2}\left({x}+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 20205 by vivek last updated on 24/Aug/17 $${find}\:{the}\:{sin}^{−\mathrm{1}} \:{diferentiation} \\ $$ Answered by Joel577 last updated on 24/Aug/17 $${y}\:=\:\mathrm{sin}^{−\mathrm{1}} \:\left({x}\right) \\ $$$${x}\:=\:\mathrm{sin}\:{y} \\…
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