Question Number 221498 by wewji12 last updated on 07/Jun/25 $$\mathrm{Solve}\:\mathrm{differantial}\:\mathrm{Equation} \\ $$$$\frac{{d}\:\:}{{dt}}\left[\frac{{dy}\left({t}\right)}{{dt}}\right]+{ty}\left({t}\right)=\mathrm{0} \\ $$ Answered by MrGaster last updated on 07/Jun/25 $${y}\left({t}\right)={C}_{\mathrm{1}} \underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{m}}…
Question Number 221558 by mr W last updated on 07/Jun/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221521 by zzjZZJ last updated on 07/Jun/25 Commented by MathematicalUser2357 last updated on 09/Jun/25 You can't mix math and chemistry. So this is undefined for mathematics and chemistry. Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221554 by Tawa11 last updated on 07/Jun/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221523 by zzjZZJ last updated on 07/Jun/25 Commented by MathematicalUser2357 last updated on 09/Jun/25 No result in range of all standard mathematical functions. I will define this integral as Q_221523(x). Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221544 by gregori last updated on 07/Jun/25 $$\:\:\sqrt[{{x}+\mathrm{1}}]{{x}−\mathrm{1}}\:=\:\sqrt[{{x}−\mathrm{1}}]{{x}+\mathrm{1}}\:,\:{x}\:{real}\: \\ $$ Answered by mr W last updated on 07/Jun/25 $${at}\:{first}\:{let}'{s}\:{have}\:{a}\:{look}\:{at}\:{the} \\ $$$${function}\:{f}\left({x}\right)={x}\mathrm{ln}\:{x}. \\ $$$${f}'\left({x}\right)=\mathrm{ln}\:{x}+\mathrm{1}=\mathrm{0}\:\Rightarrow{x}=\frac{\mathrm{1}}{{e}}…
Question Number 221513 by MrGaster last updated on 07/Jun/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221541 by PaulDirac last updated on 07/Jun/25 $$\int_{\mathrm{0}} ^{\:\pi} \mathrm{tan}\left(\mathrm{4}!\right)^{{e}^{\mathrm{3}{x}^{\mathrm{2}} +\:\mathrm{2}{x}} } .{dx} \\ $$ Answered by MrGaster last updated on 07/Jun/25 $$=\int_{\mathrm{0}}…
Question Number 221504 by ajfour last updated on 07/Jun/25 $${Find}\:{x}\:{if}\:\:\:\:\frac{{x}^{\mathrm{4}} }{\mathrm{4}^{{x}} }=\frac{\mathrm{4}^{{x}} }{{x}^{\mathrm{4}} }\:\:.\:\:\:{x}\in\mathbb{R} \\ $$ Answered by mr W last updated on 07/Jun/25 $$\frac{{x}^{\mathrm{4}}…
Question Number 221469 by Nicholas666 last updated on 06/Jun/25 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Prove}; \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\left(\sqrt{{x}\:}\:\mathrm{ln}\:\sqrt{{x}}\right)^{\mathrm{2}} }{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} \:+\:\mathrm{4}{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}^{\mathrm{4}} \:+\:\mathrm{3}{x}^{\mathrm{6}} \:+\:\mathrm{2}{x}^{\mathrm{8}} \:+\:{x}^{\mathrm{10}} }\:\:\mathrm{d}{x} \\ $$$$\:\:\:\:\:\:\:=\:\frac{\mathrm{21}}{\mathrm{1024}}\:\zeta\left(\mathrm{3}\right)\:−\:\frac{\pi^{\mathrm{3}} }{\mathrm{1024}}\:+\:\frac{\pi^{\mathrm{3}}…