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 $$\mathrm{Assume} \\ $$$$\int\frac{\left({x}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{5}}} }{{x}^{\frac{\mathrm{8}}{\mathrm{5}}} }{dx}=\frac{{p}\left({x}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{1}\right)^{\frac{{q}}{\mathrm{5}}} }{{x}^{\frac{{r}}{\mathrm{5}}} }…
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Question Number 200844 by darklord last updated on 24/Nov/23 Commented by som(math1967) last updated on 24/Nov/23 $$?? \\ $$ Commented by darklord last updated on…
Question Number 200801 by mnjuly1970 last updated on 23/Nov/23 Answered by witcher3 last updated on 24/Nov/23 $$\mathrm{introduce}\:\mathrm{erfc}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\:\sqrt{\pi}}\int_{\mathrm{0}} ^{\mathrm{x}} \mathrm{e}^{−\mathrm{t}^{\mathrm{2}} } \mathrm{dt} \\ $$$$\phi=\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}}…
Question Number 200802 by mnjuly1970 last updated on 23/Nov/23 Answered by witcher3 last updated on 23/Nov/23 $$\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\infty} \mathrm{t}^{\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{1}} \mathrm{e}^{−\mathrm{t}} \mathrm{dt},\mathrm{x}^{\mathrm{2}}…