Question Number 222567 by MrGaster last updated on 30/Jun/25 $$\mathrm{Prove}:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{\sqrt{{K}^{\mathrm{2}} +\mathrm{36}{K}'^{\mathrm{2}} }+\mathrm{6}{K}^{'} }{{K}^{\mathrm{2}} +\mathrm{36}{K}^{'\mathrm{2}} }\:}\frac{{dk}}{\:\sqrt{{k}}\left(\mathrm{1}−{k}^{\mathrm{2}} \right)^{\frac{\mathrm{2}}{\mathrm{3}}} }=\sqrt{\pi}\left(\sqrt{\mathrm{2}}−\sqrt{\frac{\mathrm{4}−\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{3}}}\right) \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{\sqrt{{K}^{\mathrm{2}}…
Question Number 222592 by Tawa11 last updated on 30/Jun/25 $$\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{cosh}^{\mathrm{4}} \left[\mathrm{n}\:\mathrm{ln}\left(\sqrt{\mathrm{2}}\:\:+\:\:\mathrm{1}\right)\right]} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222552 by mathlove last updated on 29/Jun/25 $${x}^{{x}} =\mathrm{64}\:\:\:\:\:\:,\:\:{x}=? \\ $$ Answered by mr W last updated on 29/Jun/25 $${x}\mathrm{ln}\:{x}=\mathrm{ln}\:\mathrm{64} \\ $$$$\mathrm{ln}\:{xe}^{\mathrm{ln}\:{x}} =\mathrm{6ln}\:\mathrm{2}…
Question Number 222520 by mr W last updated on 29/Jun/25 Commented by mr W last updated on 29/Jun/25 $${a}\:{ball}\:{is}\:{released}\:{at}\:{the}\:{point}\:\left({d},\:{h}\right) \\ $$$${on}\:{to}\:{the}\:{ground}\:\:{which}\:{has}\:{the}\: \\ $$$${shape}\:{of}\:{a}\:{hyperbola} \\ $$$${with}\:{equation}\:−\frac{{x}^{\mathrm{2}}…
Question Number 222521 by hu last updated on 29/Jun/25 $$−\mathrm{3}{ix}+\frac{\pi}{\mathrm{2}}+\frac{{ix}−\sqrt{\mathrm{5}\pi}}{\mathrm{6}}=\mathrm{0} \\ $$$${x}=?\: \\ $$ Commented by Rasheed.Sindhi last updated on 29/Jun/25 $$\sqrt{\mathrm{5}\pi}\:{or}\:\sqrt{\mathrm{5}}\:\pi\:? \\ $$ Answered…
Question Number 222523 by hu last updated on 29/Jun/25 $${x}+{V}−{J}\left({x}\right)\frac{{ustx}}{{zac}^{\mathrm{2}} {x}}={x}−\frac{{ustx}_{\mathrm{0}} }{\:\sqrt{{x}}\psi+\zeta\left(\frac{−\mathrm{1}+{v\%}}{\pi+\mathrm{2}}+\mathscr{L}_{{l}\left({x}\rightarrow\mathrm{0}\right)} ^{\:\:{v\%}} {X}_{\mathrm{2}{x}^{\mathrm{2}} } ^{\:\mathrm{1}} \right)} \\ $$ Answered by wewji12 last updated on…
Question Number 222516 by MrGaster last updated on 29/Jun/25 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{integer}\:{k},\mathrm{how}\:\:\mathrm{to} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{incomplete}\:\mathrm{general} \\ $$$$\mathrm{solution}\:\mathrm{for}\:\mathrm{the}\:\mathrm{non}-\mathrm{trivial}\:\mathrm{integer} \\ $$$$\mathrm{solutions}\:\mathrm{of}\:\:\mathrm{the}\:\mathrm{Diophantine}\:\mathrm{equation}: \\ $$$${a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{ka}^{\mathrm{2}} {b}^{\mathrm{2}} ={c}^{\mathrm{4}} +{d}^{\mathrm{4}} +{kc}^{\mathrm{2}} {d}^{\mathrm{2}}…
Question Number 222519 by MrGaster last updated on 29/Jun/25 $$\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 222546 by Tawa11 last updated on 29/Jun/25 Commented by Tawa11 last updated on 29/Jun/25 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{AB}. \\ $$ Commented by fantastic last updated on…
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…