Question Number 222610 by Nicholas666 last updated on 01/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}\left({e}^{\mathrm{2}\pi{n}} \:−\:\mathrm{1}\right)} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 222595 by Ghisom last updated on 01/Jul/25 $$\Omega=\int\:\frac{\mathrm{sin}^{\mathrm{2}} \:{x}\:\sqrt{\mathrm{cos}\:{x}}}{\mathrm{1}+\mathrm{3sin}^{\mathrm{2}} \:{x}}{dx} \\ $$$$\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{solve}\:\mathrm{this},\:\mathrm{maybe}\:\mathrm{some}\:\mathrm{genius}\:\mathrm{can}. \\ $$$$\mathrm{WolframAlpha}\:\mathrm{gives}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{but}\:\mathrm{I} \\ $$$$\mathrm{need}\:\mathrm{the}\:\mathrm{path}… \\ $$ Commented by MrGaster last updated…
Question Number 222567 by MrGaster last updated on 30/Jun/25 $$\mathrm{Prove}:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{\sqrt{{K}^{\mathrm{2}} +\mathrm{36}{K}'^{\mathrm{2}} }+\mathrm{6}{K}^{'} }{{K}^{\mathrm{2}} +\mathrm{36}{K}^{'\mathrm{2}} }\:}\frac{{dk}}{\:\sqrt{{k}}\left(\mathrm{1}−{k}^{\mathrm{2}} \right)^{\frac{\mathrm{2}}{\mathrm{3}}} }=\sqrt{\pi}\left(\sqrt{\mathrm{2}}−\sqrt{\frac{\mathrm{4}−\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{3}}}\right) \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{\sqrt{{K}^{\mathrm{2}}…
Question Number 222519 by MrGaster last updated on 29/Jun/25 $$\mathrm{Prove}: \\ $$$$\int_{\mathrm{0}} ^{+\infty} \sqrt{\mathrm{cosh}\:{x}}−\sqrt{\mathrm{sinh}\:{x}}{dx}=\frac{\mathrm{2}−\sqrt{\mathrm{2}}}{\:\sqrt{\pi}}\Gamma^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222541 by Nicholas666 last updated on 29/Jun/25 $$ \\ $$$$\:\:\:\mathrm{very}\:\mathrm{very}\:\mathrm{crazy}\:\mathrm{problem},\:\:\mathrm{i}\:\mathrm{am}\:\mathrm{not}\:\mathrm{found} \\ $$$$\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{result}\:\mathrm{of}\:\mathrm{this}\:\mathrm{integral}; \\ $$$$\:\:\:\:\:\:\:\:\int\frac{\mathrm{1}}{\:\sqrt{{z}}\:+\:\sqrt{{z}−{h}}\:+\:\sqrt{{z}−\mathrm{2}{h}}}\:{dz} \\ $$$$ \\ $$ Commented by Ghisom last updated…
Question Number 222529 by Nicholas666 last updated on 29/Jun/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{−{x}+\frac{\mathrm{1}}{{x}}\:} \:{dx}\:=\:?? \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 222512 by Shrodinger last updated on 28/Jun/25 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{xsinxcosx}}{{tan}^{\mathrm{2}} {x}+{cotan}^{\mathrm{2}} {x}}{dx} \\ $$ Answered by mr W last updated on 29/Jun/25 $${I}=\int_{\mathrm{0}}…
Question Number 222448 by Nicholas666 last updated on 27/Jun/25 $$ \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} +\sqrt{{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{2}} +\mathrm{4}}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$$$ \\ $$ Terms of Service…
Question Number 222422 by MrGaster last updated on 26/Jun/25 $$\mathrm{Prove}:\int_{\mathrm{0}} ^{+\infty} \frac{{x}^{\mathrm{2}} \mathrm{lnsinh}{x}}{\mathrm{cosh}\:\mathrm{3}{x}}{dx}=\frac{\mathrm{1}}{\mathrm{9}}\pi^{\mathrm{2}} {G}−\frac{\mathrm{5}}{\mathrm{108}}\pi^{\mathrm{3}} \mathrm{ln}\:\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222432 by Shrodinger last updated on 26/Jun/25 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{xsinxcosx}}{{tan}^{\mathrm{2}} {x}+{cotan}^{\mathrm{2}} {x}}{dx} \\ $$ Answered by MathematicalUser2357 last updated on 28/Jun/25 $$\mathrm{0}.\mathrm{112076} \\…