Question Number 201228 by Calculusboy last updated on 02/Dec/23 $$\int\sqrt{\boldsymbol{{x}}+\sqrt{\boldsymbol{{x}}+\sqrt{\boldsymbol{{x}}}}}\:\boldsymbol{{dx}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 201224 by Calculusboy last updated on 02/Dec/23 $$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\boldsymbol{{sinx}}}}\boldsymbol{{dx}} \\ $$ Answered by witcher3 last updated on 02/Dec/23 $$\sqrt{\mathrm{1}+\mathrm{sin}\left(\mathrm{x}\right)}=\mathrm{hint}\::\mid\mathrm{sin}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)+\mathrm{cos}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\mid \\ $$ Answered by Sutrisno…
Question Number 201227 by Calculusboy last updated on 02/Dec/23 $$\:\int\:\frac{\left(\boldsymbol{{x}}^{\mathrm{4}} +\boldsymbol{{x}}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{4}}} }{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}} \\ $$ Answered by Sutrisno last updated on 04/Dec/23 $$\:=\int\:\frac{\left(\boldsymbol{{x}}^{\mathrm{4}} \left(\mathrm{1}+\boldsymbol{{x}}^{\mathrm{3}}…
Question Number 201222 by Calculusboy last updated on 02/Dec/23 $$\:\int\:\left(\boldsymbol{{x}}^{\mathrm{6}} +\boldsymbol{{x}}^{\mathrm{9}} \right)^{\frac{\mathrm{1}}{\mathrm{6}}} \boldsymbol{{dx}} \\ $$ Answered by MathematicalUser2357 last updated on 04/Jan/24 $$\mathrm{A}\:\mathrm{function}\:\mathrm{that}\:\mathrm{contains}\:_{\mathrm{2}} {F}_{\mathrm{1}} \\…
Question Number 201223 by Calculusboy last updated on 02/Dec/23 $$\int\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\boldsymbol{{x}}}}\:\boldsymbol{{dx}} \\ $$ Answered by witcher3 last updated on 02/Dec/23 $$=\int\mathrm{2}\sqrt{\mathrm{1}+\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}}}.\frac{\mathrm{dx}}{\mathrm{2}\:\sqrt{\mathrm{1}+\mathrm{x}}} \\ $$$$=\mathrm{2}\int\sqrt{\mathrm{t}^{\mathrm{2}} +\mathrm{t}}\mathrm{dt} \\ $$$$\Leftrightarrow\int\mathrm{2}\sqrt{\left(\mathrm{t}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}}…
Question Number 201172 by Calculusboy last updated on 01/Dec/23 Answered by Sutrisno last updated on 01/Dec/23 $$=\int\frac{\mathrm{2}{e}^{\mathrm{2}{x}} −{e}^{{x}} }{\:\sqrt{\mathrm{3}\left({e}^{\mathrm{2}{x}} −\mathrm{2}{e}^{{x}} −\frac{\mathrm{1}}{\mathrm{3}}\right)}}{dx} \\ $$$$=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\int\frac{\mathrm{2}{e}^{\mathrm{2}{x}} −{e}^{{x}} }{\:\sqrt{\left({e}^{{x}}…
Question Number 201184 by Calculusboy last updated on 01/Dec/23 Answered by Sutrisno last updated on 01/Dec/23 $${misal}\::\:\:\sqrt{\mathrm{2}{x}}+\mathrm{4}={u}\rightarrow{dx}=\sqrt{\mathrm{2}{x}}{du} \\ $$$$=\int\frac{\sqrt{\mathrm{2}{x}}}{{u}}.\sqrt{\mathrm{2}{x}}{du} \\ $$$$=\int\frac{\left({u}−\mathrm{4}\right)^{\mathrm{2}} }{{u}}{du} \\ $$$$=\int\frac{{u}^{\mathrm{2}} −\mathrm{8}{u}+\mathrm{16}}{{u}}{du}…
Question Number 201110 by emilagazade last updated on 29/Nov/23 $$\int\frac{\mathrm{1}}{\:\sqrt{\left({x}−{a}\right)^{\mathrm{3}} }+\sqrt{\left({x}+{a}\right)^{\mathrm{3}} }}{dx} \\ $$ Answered by Frix last updated on 29/Nov/23 $$\sqrt{{p}}+\sqrt{{q}}=\sqrt{{p}+\mathrm{2}\sqrt{{pq}}+{q}} \\ $$$$\int\frac{{dx}}{\:\left({x}−{a}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} +\left({x}+{a}\right)^{\frac{\mathrm{3}}{\mathrm{2}}}…
Question Number 201016 by Calculusboy last updated on 28/Nov/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 201011 by Calculusboy last updated on 28/Nov/23 $$\boldsymbol{{Prove}}\:\boldsymbol{{that}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{2}\boldsymbol{{arctan}}\left(\frac{\boldsymbol{{t}}}{\boldsymbol{{x}}}\right)}{\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{\pi{t}}} −\mathrm{1}}\boldsymbol{{dt}}=\boldsymbol{{In}\Gamma}\left(\boldsymbol{{x}}\right)−\boldsymbol{{xIn}}\left(\boldsymbol{{x}}\right)+\boldsymbol{{x}}−\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{{In}}\left(\frac{\mathrm{2}\boldsymbol{\pi}}{\boldsymbol{{x}}}\right) \\ $$$$\boldsymbol{{Michael}}\:\boldsymbol{{faraday}} \\ $$ Terms of Service Privacy Policy Contact:…