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Question Number 106570 by bobhans last updated on 06/Aug/20 $$\left(\mathrm{1}\right)\underset{\mathrm{0}} {\overset{\mathrm{a}} {\int}}\:\frac{\sqrt{\mathrm{a}−\mathrm{x}}}{\:\sqrt{\mathrm{a}−\mathrm{x}}+\sqrt{\mathrm{x}}}\:\mathrm{dx}\:=? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{0}\:\:\:\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{a}}{\mathrm{2}}\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{a}\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{2a}\:\:\:\:\:\:\left(\mathrm{e}\right)\:\frac{\mathrm{5}}{\mathrm{2}}\mathrm{a} \\ $$$$\left(\mathrm{2}\right)\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\frac{\mathrm{1}−\mathrm{tan}\:\mathrm{x}}{\mathrm{1}+\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{0}\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{ln}\:\mathrm{2}\:\:\:\:\:\left(\mathrm{c}\right)\:−\mathrm{ln}\:\mathrm{2}\:\:\:\:\:\left(\mathrm{d}\right)\:\pi\mathrm{ln}\:\mathrm{2}\:\:\:\left(\mathrm{e}\right)\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mathrm{2} \\ $$$$\left(\mathrm{3}\right)\:\left(\sqrt{\mathrm{3}}+\mathrm{2}\right)^{\mathrm{x}} \:>\:\mathrm{7}−\mathrm{4}\sqrt{\mathrm{3}}\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{set} \\ $$…

Question-172088

Question Number 172088 by Mikenice last updated on 23/Jun/22 Answered by Joepkollie last updated on 23/Jun/22 $$\:\:\:\boldsymbol{{solution}}.. \\ $$$$\:\:\:\boldsymbol{{y}}=\boldsymbol{\mathrm{e}}^{\boldsymbol{{u}}\:} \Rightarrow\Rightarrow\boldsymbol{{y}}'=\boldsymbol{\mathrm{e}}^{\boldsymbol{{u}}} \bullet\boldsymbol{{u}}' \\ $$$$\:\:\:\:\boldsymbol{{y}}'=\mathrm{cos}\boldsymbol{{x}\mathrm{e}}^{\mathrm{sin}\boldsymbol{{x}}} .. \\…