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Question Number 211727 by Spillover last updated on 18/Sep/24 Answered by MrGaster last updated on 03/Nov/24 $$=\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\left(\pi−\mathrm{4}{x}\right)\mathrm{tan}\:{x}\left(\mathrm{1}+\mathrm{tan}\:{x}\right)}{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} {x}}{dx} \\ $$$$=\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\left(\pi−\mathrm{4}{x}\right)\mathrm{tan}\:{x}+\left(\pi−\mathrm{4}{x}\right)\mathrm{tan}^{\mathrm{2}} {x}}{\mathrm{cos}^{\mathrm{2}}…
Question Number 211720 by Nadirhashim last updated on 18/Sep/24 $$\:\:\:\:\:\boldsymbol{{if}}\:\:\frac{\mathrm{8}^{\boldsymbol{{x}}} −\mathrm{2}^{\boldsymbol{{x}}} }{\mathrm{6}^{\boldsymbol{{x}}} −\mathrm{3}^{\boldsymbol{{x}}} }\:\:\:=\:\mathrm{2}\:\boldsymbol{{find}}\:\boldsymbol{{x}} \\ $$ Answered by Frix last updated on 18/Sep/24 $$\mathrm{obviously}\:{x}=\mathrm{1} \\…
Question Number 211722 by hardmath last updated on 18/Sep/24 $$\mathrm{a},\:\mathrm{b}\:\in\:\mathbb{N} \\ $$$$\mathrm{a}\:\centerdot\:\mathrm{b}\:=\:\mathrm{144} \\ $$$$ \\ $$how many different numbers can a and b be here?…
Question Number 211716 by liuxinnan last updated on 18/Sep/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}×\mathrm{3}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}×\mathrm{3}×\centerdot\centerdot\centerdot×{x}}\right)=? \\ $$ Answered by BHOOPENDRA last updated on 18/Sep/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\underset{{n}=\mathrm{0}\:} {\overset{{x}} {\sum}}\frac{\mathrm{1}}{{n}!}−\mathrm{1}\right) \\…
Question Number 211717 by liuxinnan last updated on 18/Sep/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{li}{m}}\frac{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} −\mathrm{1}}{{e}^{{x}^{\mathrm{2}} } −\mathrm{1}}=? \\ $$ Answered by BHOOPENDRA last updated on 18/Sep/24 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 211719 by RojaTaniya last updated on 18/Sep/24 Commented by Frix last updated on 18/Sep/24 $${n}=\mathrm{1} \\ $$$$\mathrm{2}+\mathrm{12}+\mathrm{2011}=\mathrm{2025}=\mathrm{45}^{\mathrm{2}} \\ $$ Terms of Service Privacy…
Question Number 211708 by Skyneless last updated on 17/Sep/24 Answered by Frix last updated on 18/Sep/24 $$\int\sqrt{\mathrm{tan}\:{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{2tan}^{−\mathrm{1}} \:\sqrt{\mathrm{tan}\:{x}}\right] \\ $$$$=\int\frac{\mathrm{1}−\mathrm{cos}\:{t}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \:{t}}{dt} \\ $$$$…
Question Number 211706 by Nadirhashim last updated on 17/Sep/24 $$\:\:\:\:\:\boldsymbol{{if}}\:\:\boldsymbol{{x}}^{\boldsymbol{{log}}\mathrm{27}} +\:\:\:\mathrm{9}^{\boldsymbol{{logx}}} =\mathrm{36}\:\boldsymbol{{find}}\:\boldsymbol{{x}} \\ $$ Answered by mehdee7396 last updated on 17/Sep/24 $${x}^{\mathrm{3}{log}\mathrm{3}} +{x}^{\mathrm{2}{log}\mathrm{3}} =\mathrm{36}\:\: \\…