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Question Number 119891 by sdfg last updated on 27/Oct/20 $${show}\:{that}\: \\ $$$$\frac{{d}}{{dx}}\:\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty} {t}^{{x}−\mathrm{1}} {e}^{−{t}} {lnt}\:{dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 185420 by Ml last updated on 21/Jan/23 Commented by Frix last updated on 21/Jan/23 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{this}\:\mathrm{can}\:\mathrm{be}\:\mathrm{simplified}. \\ $$ Answered by malwan last updated on…

Question Number 185422 by Ml last updated on 21/Jan/23 Answered by hmr last updated on 21/Jan/23 $$\mathrm{2}\sqrt{\mathrm{5}}\:=\:\sqrt{\mathrm{20}}\:=\:\left(\mathrm{20}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\rightarrow{a}=\:\sqrt[{\mathrm{5}}]{\mathrm{2}\sqrt{\mathrm{5}}}\:=\:\sqrt[{\mathrm{5}}]{\left(\mathrm{20}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} }\:=\:\left(\mathrm{20}\right)^{\frac{\mathrm{1}}{\mathrm{10}}} \\ $$$$ \\ $$$$\sqrt[{\mathrm{3}}]{{a}^{\mathrm{16}} }\:=\:{a}^{\frac{\mathrm{16}}{\mathrm{3}}}…

Question Number 185413 by Safiullah_21 last updated on 21/Jan/23 $$\mathrm{2}^{{x}} ={a} \\ $$$$ \\ $$ Answered by alephzero last updated on 21/Jan/23 $$\mathrm{2}^{{x}} \:=\:{a} \\…

Question Number 119839 by ZiYangLee last updated on 27/Oct/20 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{sin}\:{x}−\mathrm{cos}^{\mathrm{2}} {x}+\mathrm{sin}^{\mathrm{3}} {x}−\mathrm{cos}^{\mathrm{4}} {x}+\mathrm{sin}^{\mathrm{5}} {x}−\mathrm{cos}^{\mathrm{6}} {x} \\ $$$$+\mathrm{sin}^{\mathrm{7}} {x}−\mathrm{cos}^{\mathrm{8}} {x}+\ldots\ldots=\sqrt{\mathrm{2}}−\mathrm{1} \\ $$ Answered by…