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}} \\ $$$$\int\frac{{dx}}{\:\left({x}−{a}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} +\left({x}+{a}\right)^{\frac{\mathrm{3}}{\mathrm{2}}}…
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Question Number 201011 by Calculusboy last updated on 28/Nov/23 $$\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:…
Question Number 201044 by mnjuly1970 last updated on 28/Nov/23 $$ \\ $$$$\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \left({x}−{y}\:\right)^{\mathrm{2}} {sin}^{\:\mathrm{2}} \:\left(\:{x}+{y}\:\right){dxdy}=? \\ $$ Answered by mathematicsmagic last updated…
Question Number 200933 by Spillover last updated on 26/Nov/23 $$ \\ $$$$\int\mathrm{coth}\:\left(\mathrm{ln}\:\left[\sqrt{\mathrm{tanh}\:\left(\mathrm{ln}\:\left(\sqrt{\mathrm{sec}^{−\mathrm{1}} \:\:\sqrt[{\mathrm{4}}]{{x}}\:\:}\right)\right)}\:\right]\right) \\ $$$$ \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 200930 by Spillover last updated on 26/Nov/23 $${If}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{4}} \right)^{{n}} {dx}\:\:{and}\:\:\frac{{I}_{{n}} }{{I}_{{n}−\mathrm{1}} }=\frac{\lambda{n}}{\lambda{n}+\mathrm{1}} \\ $$$${then}\:{find}\:\:\lambda \\ $$ Commented by mr W…
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Question Number 200915 by Rupesh123 last updated on 26/Nov/23 Answered by Frix last updated on 26/Nov/23 $$\mathrm{Assume} \\ $$$$\int\frac{\left({x}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{5}}} }{{x}^{\frac{\mathrm{8}}{\mathrm{5}}} }{dx}=\frac{{p}\left({x}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{1}\right)^{\frac{{q}}{\mathrm{5}}} }{{x}^{\frac{{r}}{\mathrm{5}}} }…