Question Number 221585 by mr W last updated on 08/Jun/25 $${solve}\:{for}\:{x}\:\in{R} \\ $$$$\left({x}^{\mathrm{3}} −\mathrm{6}\right)^{\mathrm{3}} ={x}+\mathrm{6} \\ $$ Commented by mr W last updated on 08/Jun/25…
Question Number 221618 by fantastic last updated on 08/Jun/25 $${solve}\:{for}\:{x} \\ $$$$\mathrm{2}^{{x}} +\mathrm{4}^{{x}} =\mathrm{8}^{{x}} \\ $$ Answered by MathematicalUser2357 last updated on 09/Jun/25 $$\mathrm{log}_{\mathrm{2}} \phi…
Question Number 221586 by Nicholas666 last updated on 08/Jun/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{1}\:+\:\mathrm{3}{x}\:}\:{dx} \\ $$$$ \\ $$ Answered by MrGaster last updated on 08/Jun/25 Commented by…
Question Number 221587 by Tawa11 last updated on 08/Jun/25 $$\int_{\:\mathrm{2}} ^{\:\mathrm{3}} \:\frac{\mathrm{tan}^{−\:\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{1}\:\:−\:\:\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Answered by maths2 last updated on 09/Jun/25 $$=\int_{\mathrm{2}} ^{\mathrm{3}}…
Question Number 221582 by MrGaster last updated on 08/Jun/25 $$\left(\mathrm{1}\right):\int_{\mathrm{0}} ^{{u}} {x}^{\nu−\mathrm{1}} \left({u}^{\mathrm{2}} −{x}^{\mathrm{2}} \right)^{\varrho−\mathrm{1}} {e}^{\mu{x}} {dx}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mu^{{n}} }{{n}!}\int_{\mathrm{0}} ^{{u}} {x}^{\nu+{n}−\mathrm{1}} \left({u}^{\mathrm{2}} −{x}^{\mathrm{2}} \right)^{\varrho−\mathrm{1}}…
Question Number 221583 by MrGaster last updated on 08/Jun/25 Answered by MrGaster last updated on 08/Jun/25 $$=\int_{\mathrm{0}} ^{\mathrm{1}} {t}^{\mathrm{1}/\mathrm{11}−\mathrm{1}} \left(\mathrm{1}−{t}\right)^{\mathrm{9}/\mathrm{11}−\mathrm{1}} \beta\left(\frac{\:\mathrm{1}}{\mathrm{11}},\frac{\mathrm{9}}{\mathrm{11}}\right)\Gamma\left(\frac{\mathrm{1}}{\mathrm{11}}\right)\Gamma\left(\frac{\mathrm{9}}{\mathrm{11}}\right)\left(\int_{\mathrm{0}} ^{\mathrm{1}} {s}^{\mathrm{3}/\mathrm{11}−\mathrm{1}} \left(\mathrm{1}−{s}\right)^{\mathrm{5}/\mathrm{11}−\mathrm{1}} \beta\left(\frac{\mathrm{3}}{\mathrm{11}},\frac{\mathrm{5}}{\mathrm{11}}\right)\Gamma\left(\frac{\mathrm{3}}{\mathrm{11}}\right)\Gamma\left(\frac{\mathrm{5}}{\mathrm{11}}\right)\int_{\mathrm{0}}…
Question Number 221576 by MrGaster last updated on 08/Jun/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 221577 by Nicholas666 last updated on 08/Jun/25 $$ \\ $$$$\:\:\:\:\:\:\mathrm{Prove};\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{x}\mathrm{d}{x}}{\left({x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\left({e}^{\mathrm{2}\pi{x}} \:−\:\mathrm{1}\right)}\:=\:\frac{\gamma}{\mathrm{2}}\:−\:\frac{\mathrm{1}}{\mathrm{4}}\:\: \\ $$$$\:\:\:\:\mathrm{where};\:\gamma\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{Euler}'\mathrm{s}\:\mathrm{Mascheroni}\:\mathrm{constant}\:\:\:\: \\ $$$$ \\ $$ Answered by MrGaster…
Question Number 221578 by efronzo1 last updated on 08/Jun/25 $$\:\:\: \\ $$ Answered by gregori last updated on 08/Jun/25 $$\:\:\underbrace{\:}\: \\ $$ Terms of Service…
Question Number 221637 by ASAD7391 last updated on 08/Jun/25 Answered by fantastic last updated on 09/Jun/25 $${let}\:\angle{A}=\theta\:\therefore\angle{B}=\mathrm{2}\theta\: \\ $$$${but}\:\angle{A}+\angle{B}+\angle{C}=\mathrm{180}^{\mathrm{0}} \\ $$$${or}\:\theta+\mathrm{2}\theta=\mathrm{180}^{\mathrm{0}} −\mathrm{90}^{\mathrm{0}} =\mathrm{90}^{\mathrm{0}} \\ $$$${or}\:\theta=\frac{\mathrm{90}^{\mathrm{0}}…