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Author: Tinku Tara

sin-2x-1-sin-3x-dx-

Question Number 221601 by Nicholas666 last updated on 08/Jun/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\frac{{sin}\:\mathrm{2}{x}}{\mathrm{1}\:+\:{sin}\:\mathrm{3}{x}}\:{dx} \\ $$$$ \\ $$ Answered by Frix last updated on 08/Jun/25 $$=−\mathrm{2}\int\frac{\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}}{\mathrm{4sin}^{\mathrm{3}} \:{x}\:−\mathrm{3sin}\:{x}\:+\mathrm{1}}{dx}\:\overset{\left[{t}=\mathrm{sin}\:{x}\right]}…

solve-for-x-a-a-x-a-a-x-2x-it-s-possible-to-solve-for-a-but-x-seems-impossible-to-me-

Question Number 221501 by Jyrgen last updated on 07/Jun/25 $${solve}\:{for}\:\mathrm{x}: \\ $$$$\sqrt{\mathrm{a}−\sqrt{\mathrm{a}+\mathrm{x}}}+\sqrt{\mathrm{a}+\sqrt{\mathrm{a}−\mathrm{x}}}=\mathrm{2x} \\ $$$${it}'{s}\:{possible}\:{to}\:{solve}\:{for}\:\mathrm{a}\:{but}\:\mathrm{x}\:{seems} \\ $$$${impossible}\:{to}\:{me} \\ $$ Answered by ajfour last updated on 07/Jun/25…

Solve-differantial-Equation-d-dt-dy-t-dt-ty-t-0-

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}}…

x-1-1-x-1-x-1-1-x-1-x-real-

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}}…