Question Number 211796 by Spillover last updated on 21/Sep/24 Answered by Ghisom last updated on 21/Sep/24 $$\int\sqrt{\frac{\mathrm{cos}\:\left({x}−{a}\right)}{\mathrm{sin}\:\left({x}+{a}\right)}}{dx}= \\ $$$$=\int\sqrt{\frac{\mathrm{cos}\:{a}\:\mathrm{cos}\:{x}\:+\mathrm{sin}\:{a}\:\mathrm{sin}\:{x}}{\mathrm{sin}\:{a}\:\mathrm{cos}\:{x}\:+\mathrm{cos}\:{a}\:\mathrm{sin}\:{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:{x}\right] \\ $$$$=\int\sqrt{\frac{{t}\mathrm{sin}\:{a}\:+\mathrm{cos}\:{a}}{{t}\mathrm{cos}\:{a}\:+\mathrm{sin}\:{a}}}×\frac{{dt}}{{t}^{\mathrm{2}} +\mathrm{1}}= \\…
Question Number 211798 by Spillover last updated on 21/Sep/24 Answered by Ghisom last updated on 22/Sep/24 $$\frac{\mathrm{e}^{\mathrm{cos}\:{x}} \left({x}\mathrm{sin}^{\mathrm{3}} \:{x}\:+\mathrm{cos}\:{x}\right)}{\mathrm{sin}^{\mathrm{2}} \:{x}}= \\ $$$$=\mathrm{e}^{\mathrm{cos}\:{x}} {x}\mathrm{sin}\:{x}\:+\frac{\mathrm{e}^{\mathrm{cos}\:{x}} \mathrm{cos}\:{x}}{\mathrm{sin}^{\mathrm{2}} \:{x}}=…
Question Number 211797 by Spillover last updated on 21/Sep/24 Answered by Ghisom last updated on 21/Sep/24 $$\int\frac{\sqrt{\mathrm{cot}\:{x}}−\sqrt{\mathrm{tan}\:{x}}}{\mathrm{1}+\mathrm{3sin}\:\mathrm{2}{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{tan}\:{x}}\right] \\ $$$$=−\mathrm{2}\int\frac{{t}^{\mathrm{2}} −\mathrm{1}}{{t}^{\mathrm{4}} +\mathrm{6}{t}^{\mathrm{2}} +\mathrm{1}}{dt}= \\…
Question Number 211787 by hardmath last updated on 20/Sep/24 $$\mathrm{Compare}: \\ $$$$ \\ $$$$\mathrm{5}^{\mathrm{100}} \:,\:\mathrm{6}^{\mathrm{91}} \:,\:\mathrm{7}^{\mathrm{90}} \:,\:\mathrm{8}^{\mathrm{85}} \\ $$ Terms of Service Privacy Policy Contact:…
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Question Number 211761 by MATHEMATICSAM last updated on 20/Sep/24 $$\mathrm{If}\:{x}\:=\:\frac{\mathrm{4}{a}^{\mathrm{2}} {b}}{\mathrm{4}{b}^{\mathrm{2}} \:+\:\mathrm{1}}\:\mathrm{where}\:{b}\:>\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{then} \\ $$$$\frac{\sqrt{{a}^{\mathrm{2}} \:+\:{x}}\:+\:\sqrt{{a}^{\mathrm{2}} \:−\:{x}}}{\:\sqrt{{a}^{\mathrm{2}} \:+\:{x}}\:−\:\sqrt{{a}^{\mathrm{2}} \:−\:{x}}}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 211727 by Spillover last updated on 18/Sep/24 Answered by MrGaster last updated on 03/Nov/24 $$=\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\left(\pi−\mathrm{4}{x}\right)\mathrm{tan}\:{x}\left(\mathrm{1}+\mathrm{tan}\:{x}\right)}{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} {x}}{dx} \\ $$$$=\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\left(\pi−\mathrm{4}{x}\right)\mathrm{tan}\:{x}+\left(\pi−\mathrm{4}{x}\right)\mathrm{tan}^{\mathrm{2}} {x}}{\mathrm{cos}^{\mathrm{2}}…
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Question Number 211722 by hardmath last updated on 18/Sep/24 $$\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 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} \\…