Question Number 223786 by Nicholas666 last updated on 04/Aug/25 $$ \\ $$$$\:\:\:\:\boldsymbol{\mathrm{Evaluate}}\:;\:\int\:\sqrt{\:\boldsymbol{\mathrm{tan}}\:\boldsymbol{{x}}}\:\boldsymbol{\mathrm{d}{x}}\:,\:\boldsymbol{\mathrm{Using}}\:\boldsymbol{\mathrm{feynman}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{trick}} \\ $$$$ \\ $$ Commented by Frix last updated on 05/Aug/25 $$\mathrm{I}'\mathrm{ll}\:\mathrm{do}\:\mathrm{it}\:\mathrm{but}\:\mathrm{only}\:\mathrm{if}\:\mathrm{you}\:\mathrm{solve} \\…
Question Number 223728 by Nicholas666 last updated on 03/Aug/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}_{\:} } ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+\sqrt{{x}}\right)\centerdot\mathrm{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+\sqrt{{x}}}\:\mathrm{d}{x} \\ $$ Answered by Tawa11 last updated on 14/Aug/25 $$\mathrm{Finally}:…
Question Number 223631 by MathematicalUser2357 last updated on 01/Aug/25 Commented by MathematicalUser2357 last updated on 01/Aug/25 $$\mathrm{Find}\:{F}\left({x}\right) \\ $$ Answered by Frix last updated on…
Question Number 223580 by Nicholas666 last updated on 30/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}\:} \:\frac{{e}^{−\boldsymbol{{r}}^{\mathrm{2}} } \boldsymbol{\mathrm{sin}}\left(\mathrm{1}/\boldsymbol{{r}}^{\mathrm{2}} \right)\boldsymbol{\mathrm{ln}}\left(\boldsymbol{{r}}+\mathrm{1}\right)}{\boldsymbol{{r}}^{\mathrm{2}} }\:\boldsymbol{\mathrm{d}{r}} \\ $$$$ \\ $$ Answered by MathematicalUser2357…
Question Number 223534 by Tawa11 last updated on 28/Jul/25 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}}\:\mathrm{ln}^{\mathrm{3}} \left(\frac{\mathrm{1}\:\:−\:\:\mathrm{x}}{\mathrm{1}\:\:+\:\:\mathrm{x}}\right)\:\mathrm{dx} \\ $$ Answered by MathematicalUser2357 last updated on 31/Jul/25 $$\:\cancel{\:} \\ $$…
Question Number 223525 by Nicholas666 last updated on 27/Jul/25 $$ \\ $$$$\:\:\:\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \int_{\mathrm{0}} ^{\mathrm{2}\pi} \int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\mid\:\mathrm{cos}\:{x}\:+\:\mathrm{cos}\:{y}\:+\:\mathrm{cos}\:{z}\:\:\mid\:\:{dxdydz}\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service…
Question Number 223461 by MathematicalUser2357 last updated on 26/Jul/25 Answered by mr W last updated on 26/Jul/25 Commented by mr W last updated on 26/Jul/25…
Question Number 223368 by Nicholas666 last updated on 22/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\boldsymbol{\mathrm{ln}}\left(\frac{\mathrm{2}\:\boldsymbol{\mathrm{cos}}\left({x}^{\mathrm{2}} \right)\:+\:\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \left({x}/\mathrm{2}\right)}{\mathrm{1}\:+\:\boldsymbol{\mathrm{cos}}\:\left({x}/\mathrm{2}\right)}\right)\:\boldsymbol{\mathrm{d}}{x} \\ $$$$ \\ $$ Answered by MathematicalUser2357 last updated…
Question Number 223367 by Nicholas666 last updated on 22/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\mathrm{ln}\left(\mathrm{2}\:\mathrm{cos}\left({x}^{\mathrm{2}} \right)\:+\:\mathrm{ln}^{\mathrm{2}} \:\left(\frac{{x}}{\mathrm{2}}\right)\:\mathrm{d}{x}\right. \\ $$$$ \\ $$ Commented by MathematicalUser2357 last updated…
Question Number 223304 by Nadirhashim last updated on 21/Jul/25 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\underset{\mathrm{0}} {\overset{{x}^{\mathrm{2}} } {\int}}\boldsymbol{{sin}}\left(\sqrt{\boldsymbol{{t}}}\right)\boldsymbol{{dt}}\:}{\boldsymbol{{x}}^{\mathrm{3}} }\:=…? \\ $$ Answered by Raphael254 last updated on 21/Jul/25 $$…