Question Number 203434 by sonukgindia last updated on 19/Jan/24 Answered by witcher3 last updated on 20/Jan/24 $$=\int\frac{−\mathrm{2sin}\left(\mathrm{2x}\right)\mathrm{sin}\left(\mathrm{3x}\right)}{\mathrm{1}+\mathrm{2cos}\left(\mathrm{3x}\right)}\mathrm{dx} \\ $$$$=\frac{\mathrm{sin}\left(\mathrm{2x}\right)}{\mathrm{3}}\mathrm{ln}\left(\mathrm{1}+\mathrm{2cos}\left(\mathrm{3x}\right)\right)−\frac{\mathrm{1}}{\mathrm{6}}\int\mathrm{sin}\left(\mathrm{x}\right)\mathrm{cos}\left(\mathrm{x}\right)\mathrm{ln}\left(\mathrm{1}+\mathrm{2cos}\left(\mathrm{3x}\right)\right)\mathrm{dx} \\ $$$$\mathrm{ln}\left(\mathrm{1}+\mathrm{2cos}\left(\mathrm{3x}\right)\right)=\mathrm{ln}\left(\mathrm{1}+\mathrm{2cos}\left(\mathrm{x}\right)\left(\mathrm{2cos}^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{1}\right)−\mathrm{4}\left(\mathrm{1}−\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)\right)\mathrm{cos}\left(\mathrm{x}\right)\right) \\ $$$$=\mathrm{ln}\left(\mathrm{1}+\mathrm{8cos}^{\mathrm{3}}…
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Question Number 203428 by cortano12 last updated on 19/Jan/24 $$\:\cancel{\underbrace{\:}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203457 by DEGWE last updated on 19/Jan/24 Answered by witcher3 last updated on 19/Jan/24 $$\mathrm{tanh}\left(\mathrm{x}\right)=\frac{\mathrm{e}^{\mathrm{2x}} −\mathrm{1}}{\mathrm{e}^{\mathrm{2x}} +\mathrm{1}} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\frac{\frac{\mathrm{1}+\mathrm{3}^{\mathrm{x}} +\mathrm{x}^{\mathrm{3}} +\mathrm{sh}\left(\mathrm{x}\right)}{\mathrm{1}−\mathrm{3}^{\mathrm{x}} −\mathrm{x}^{\mathrm{3}} −\mathrm{sh}\left(\mathrm{x}\right)}−\mathrm{1}}{\frac{\mathrm{1}+\mathrm{3}^{\mathrm{x}}…
Question Number 203389 by sonukgindia last updated on 18/Jan/24 Answered by mr W last updated on 18/Jan/24 Commented by mr W last updated on 18/Jan/24…
Question Number 203416 by Spillover last updated on 18/Jan/24 Answered by a.lgnaoui last updated on 19/Jan/24 $$\:\: \\ $$$$\:\:\:\boldsymbol{\mathrm{R}}=\mathrm{2}\boldsymbol{\mathrm{r}}+\boldsymbol{\mathrm{BM}}\mathrm{cos}\:\boldsymbol{\alpha}\:\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\:\:\:\:\boldsymbol{\mathrm{BM}}\mathrm{sin}\:\boldsymbol{\alpha}=\boldsymbol{\mathrm{r}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{2}\right) \\ $$$$\: \\ $$$$\Rightarrow\:\:\begin{cases}{\mathrm{cos}\:\boldsymbol{\alpha}=\frac{\boldsymbol{\mathrm{R}}−\mathrm{2}\boldsymbol{\mathrm{r}}}{\boldsymbol{\mathrm{BM}}}}\\{\mathrm{sin}\:\boldsymbol{\alpha}=\frac{\boldsymbol{\mathrm{r}}}{\:\boldsymbol{\mathrm{BM}}}}\end{cases}…
Question Number 203417 by hardmath last updated on 18/Jan/24 $$\mathrm{If} \\ $$$$\mid\overline {−\mathrm{z}\:+\:\boldsymbol{\mathrm{i}}\mathrm{z}}\mid\:=\:\mathrm{2}\:\sqrt{\mathrm{13}}\:\:\:\mathrm{and}\:\:\:\mathrm{z}\:=\:\mathrm{1}\:+\:\left(\mathrm{x}\:+\:\mathrm{1}\right)\centerdot\boldsymbol{\mathrm{i}} \\ $$$$ \\ $$$$\mathrm{Find}:\:\:\:\mathrm{mun}\left(\mathrm{x}\right)\:=\:? \\ $$ Commented by hardmath last updated on…
Question Number 203385 by patrice last updated on 18/Jan/24 Answered by Mathspace last updated on 18/Jan/24 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\mathrm{1}+{x}^{\mathrm{3}} }\:\Rightarrow{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \sum_{{n}=\mathrm{0}} ^{\infty} \left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{3}{n}}…
Question Number 203419 by essaad last updated on 18/Jan/24 Commented by mr W last updated on 18/Jan/24 $${question}\:{is}\:{wrong}!\:{you}\:{can}\:{not} \\ $$$${determine}\:\alpha\:{uniquely}. \\ $$ Commented by essaad…
Question Number 203387 by Noorzai last updated on 18/Jan/24 Answered by Rasheed.Sindhi last updated on 18/Jan/24 $$\mathrm{S}=\frac{\underset{{n}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\sqrt{\mathrm{10}+\sqrt{{n}}}\:}{\underset{{n}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\sqrt{\mathrm{10}−\sqrt{{n}}}\:} \\ $$$$\mathrm{S}=\frac{\underset{{n}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\frac{\sqrt{\mathrm{100}−{n}}\:}{\:\sqrt{\mathrm{10}−\sqrt{{n}}}}}{\underset{{n}=\mathrm{1}}…