Question Number 201544 by sonukgindia last updated on 08/Dec/23 Answered by aleks041103 last updated on 09/Dec/23 $${J}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{4}{sin}^{\mathrm{2}} \left({ln}\left({x}\right)\right)}{{ln}\left(\mathrm{1}/{x}\right)}{dx}=−\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{4}{sin}^{\mathrm{2}} \left(\mathrm{1}.{ln}\left({x}\right)\right)}{{ln}\left({x}\right)}{dx} \\ $$$${I}\left({s}\right)=−\int_{\mathrm{0}}…
Question Number 201545 by Calculusboy last updated on 08/Dec/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 201546 by Calculusboy last updated on 08/Dec/23 $$\:\:\:\int\boldsymbol{{Sin}}\left(\boldsymbol{{Inx}}\right)\boldsymbol{{dx}} \\ $$ Commented by aleks041103 last updated on 09/Dec/23 $${is}\:{this}\:{sine}\:{of}\:{natural}\:{log}\:{of}\:{x}\:{or}\:{sth}\:{else}? \\ $$ Commented by Calculusboy…
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Question Number 201547 by Calculusboy last updated on 08/Dec/23 Answered by mr W last updated on 08/Dec/23 $${let}\:{t}=\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}+{x} \\ $$$$\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}−{x}\right){t}=\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}−{x}\:\right)\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}+{x}\right)=\mathrm{2} \\…
Question Number 201515 by sonukgindia last updated on 08/Dec/23 Answered by Calculusboy last updated on 08/Dec/23 $$\boldsymbol{{Solution}}:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\mathrm{1}}{\mathrm{1}+\left(\frac{\mathrm{1}}{\boldsymbol{{tanx}}}\right)^{\sqrt{\mathrm{2}}} }\boldsymbol{{dx}}\:\:\Leftrightarrow\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\mathrm{1}}{\frac{\left(\boldsymbol{{tanx}}\right)^{\sqrt{\mathrm{2}}} +\mathrm{1}}{\left(\boldsymbol{{tanx}}\right)^{\sqrt{\mathrm{2}}} }}\boldsymbol{{dx}} \\…
Question Number 201510 by Calculusboy last updated on 08/Dec/23 Answered by MathematicalUser2357 last updated on 04/Jan/24 $$=−\mathrm{2tan}^{−\mathrm{1}} \left[\mathrm{cos}\left\{\frac{\mathrm{1}}{\mathrm{2}}\left({t}−\mathrm{sin}\:{t}\right)\right\}\mathrm{cosec}\left\{\frac{\mathrm{1}}{\mathrm{2}}\left({t}−\mathrm{sin}\:{t}\right)\right\}\right]+{C} \\ $$ Terms of Service Privacy Policy…
Question Number 201502 by necx122 last updated on 07/Dec/23 $${A}\:{generation}\:{is}\:{about}\:{one}-{third}\:{of}\:{a} \\ $$$${lifetime}.{Approximately}\:{about}\:{how} \\ $$$${many}\:{generations}\:{have}\:{passed}\:{since} \\ $$$${the}\:{year}\:\mathrm{0}{AD}? \\ $$ Commented by AST last updated on 07/Dec/23…
Question Number 201495 by Rodier97 last updated on 07/Dec/23 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\left({Un}\right)_{{n}\geqslant\mathrm{1}\:;} \:\:\:\:\frac{\mathrm{1}}{{nC}_{\mathrm{2}{n}} ^{{n}} \:} \\ $$$$ \\ $$$$\:\:\:\:{study}\:\:{convergence}…
Question Number 201491 by tri26112004 last updated on 07/Dec/23 $$\mathrm{1}.\:{x}^{\mathrm{2}} −\mathrm{1}+\sqrt[{\mathrm{3}}]{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} }=\mathrm{10}{x} \\ $$$$\mathrm{2}.\:\sqrt{{x}−\frac{\mathrm{1}}{{x}}}+\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}={x} \\ $$$$\mathrm{3}.\:\sqrt{\mathrm{2}{x}−\frac{\mathrm{8}}{{x}}}+\mathrm{2}\sqrt{\mathrm{1}−\frac{\mathrm{2}}{{x}}}\geqslant{x} \\ $$$$\mathrm{4}.\:\sqrt{{x}^{\mathrm{2}} +{x}}+\sqrt{{x}+\mathrm{2}}\geqslant\sqrt{\mathrm{3}\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}\right)} \\ $$$$\mathrm{5}.\:\left(\sqrt{{x}+\mathrm{5}}−\sqrt{{x}−\mathrm{3}}\right)\left(\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{15}}\right)\geqslant\mathrm{8} \\…