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Category: Integration

Evaluate-tan-x-dx-Using-feynman-s-trick-

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} \\…

0-1-ln-1-x-ln-1-x-1-x-dx-

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}:…

0-1-e-r-2-sin-1-r-2-ln-r-1-r-2-dr-

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…

0-1-ln-x-x-ln-3-1-x-1-x-dx-

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 $$\:\cancel{\:} \\ $$…

0-1-ln-2-cos-x-2-ln-2-x-2-1-cos-x-2-dx-

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…

lim-x-0-0-x-2-sin-t-dt-x-3-

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 $$…