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Author: Tinku Tara

1-0-u-x-1-u-2-x-2-1-e-x-dx-n-0-n-n-0-u-x-n-1-u-2-x-2-1-dx-n-0-n-n-u-2-n-2-2-B-n-2-u-2-2-2-n-0-n-

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-221583

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}}…

Prove-0-1-xdx-x-2-1-e-2pix-1-2-1-4-where-is-a-Euler-s-Mascheroni-constant-

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-221637

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}}…

sin-2x-1-sin-3x-dx-

Question Number 221601 by Nicholas666 last updated on 08/Jun/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\frac{{sin}\:\mathrm{2}{x}}{\mathrm{1}\:+\:{sin}\:\mathrm{3}{x}}\:{dx} \\ $$$$ \\ $$ Answered by Frix last updated on 08/Jun/25 $$=−\mathrm{2}\int\frac{\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}}{\mathrm{4sin}^{\mathrm{3}} \:{x}\:−\mathrm{3sin}\:{x}\:+\mathrm{1}}{dx}\:\overset{\left[{t}=\mathrm{sin}\:{x}\right]}…

solve-for-x-a-a-x-a-a-x-2x-it-s-possible-to-solve-for-a-but-x-seems-impossible-to-me-

Question Number 221501 by Jyrgen last updated on 07/Jun/25 $${solve}\:{for}\:\mathrm{x}: \\ $$$$\sqrt{\mathrm{a}−\sqrt{\mathrm{a}+\mathrm{x}}}+\sqrt{\mathrm{a}+\sqrt{\mathrm{a}−\mathrm{x}}}=\mathrm{2x} \\ $$$${it}'{s}\:{possible}\:{to}\:{solve}\:{for}\:\mathrm{a}\:{but}\:\mathrm{x}\:{seems} \\ $$$${impossible}\:{to}\:{me} \\ $$ Answered by ajfour last updated on 07/Jun/25…