Question Number 222812 by MrGaster last updated on 08/Jul/25 Answered by MrGaster last updated on 08/Jul/25 $${x}=\mathrm{sinh}\:{u}\Rightarrow{dx}=\mathrm{cosh}\:{udu},\sqrt{\mathrm{1}+{u}^{\mathrm{2}} }=\mathrm{cosh}\:{u} \\ $$$${u}\mid_{{x}=\mathrm{0}} =\mathrm{0},{u}\mid_{{x}=\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{sinh}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$${u}=\mathrm{sinh}^{−\mathrm{1}}…
Question Number 222811 by MrGaster last updated on 08/Jul/25 $$\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{2}{x}\right)}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by MrGaster last updated on 08/Jul/25 Terms of Service…
Question Number 222805 by MrGaster last updated on 08/Jul/25 $$\mathrm{Prove}:\int_{−\infty} ^{\infty} {J}_{\mathrm{0}} \left(\mathrm{2}{x}\right){dx}=\mathrm{1} \\ $$ Answered by MrGaster last updated on 08/Jul/25 $${J}_{\mathrm{0}} \left(\mathrm{2}{x}\right)=\frac{\mathrm{1}}{\mathrm{2}\pi}\int_{−\pi} ^{\pi}…
Question Number 222779 by mnjuly1970 last updated on 07/Jul/25 Answered by gabthemathguy25 last updated on 08/Jul/25 $$\mathrm{this}\:\mathrm{is}\:\mathrm{actually}\:\mathrm{hard}.. \\ $$$$\mathrm{im}\:\mathrm{approximating}\:\mathrm{this}. \\ $$$$\approx−\mathrm{0}.\mathrm{0491713} \\ $$ Terms of…
Question Number 222787 by Nicholas666 last updated on 07/Jul/25 $$ \\ $$$$\:\:\:\:\:\int_{\mathrm{1}} ^{\:\pi/\mathrm{2}} \:\:\frac{\mathrm{4}^{−{x}} \:\centerdot\:{e}^{\mathrm{tan}\left({x}+{x}^{\mathrm{2}} \right)} \centerdot\:\mathrm{ln}\left(\mathrm{1}\:+\:{x}^{\mathrm{3}} \right)}{\mathrm{1}\:+\:{x}}\:\:\mathrm{d}{x}\:\:\:\:\: \\ $$$$ \\ $$ Answered by gabthemathguy25…
Question Number 222705 by MrGaster last updated on 05/Jul/25 $$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}{x}\mathrm{arctan}{x}}{{x}}{dx} \\ $$ Answered by gabthemathguy25 last updated on 05/Jul/25 $${this}\:{is}\:{non}\:{elementary}\:{however}\:{i}\:{can}\:{still}\:{evaluate}\:{this} \\ $$$$\mathrm{tan}^{−\mathrm{1}} =\underset{{n}\:=\:\mathrm{0}}…
Question Number 222644 by MrGaster last updated on 03/Jul/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222607 by MrGaster last updated on 01/Jul/25 $$\mathrm{Prove}:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{3}} }{\mathrm{5}−{x}^{\mathrm{3}} }\centerdot\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}^{\mathrm{3}} }}{dx}=\frac{\sqrt[{\mathrm{3}}]{\mathrm{10}}−\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\pi \\ $$ Answered by MrGaster last updated on 01/Jul/25 $${t}={x}^{\mathrm{3}}…
Question Number 222613 by Nicholas666 last updated on 01/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\mathrm{what}\:\mathrm{is}\:\:{I}\:=\:\int\:\mathrm{tan}\:\left(\frac{\mathrm{cos}\:{x}}{{x}}\right)\:\mathrm{d}{x}\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222614 by Nicholas666 last updated on 01/Jul/25 $$ \\ $$$$\:\:\mathrm{complicated}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\mathrm{tan}\left(\frac{\mathrm{cos}\:{x}}{{x}}\right)^{\mathrm{13}} \:\mathrm{d}{x} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…