Question Number 223034 by MrGaster last updated on 13/Jul/25 $$ \\ $$$$\int\frac{{x}\:\mathrm{arctan}{xdx}}{\:\sqrt{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{k}'^{\mathrm{2}} {x}^{\mathrm{2}} \right)}}=\frac{\mathrm{1}}{{k}^{\mathrm{2}} }\left[{F}\left(\frac{\pi}{\mathrm{4}},{k}\right)−\frac{\pi}{\mathrm{2}\sqrt{\mathrm{2}\left(\mathrm{1}+{k}'\mathrm{2}\right)}}\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 223054 by Silver last updated on 13/Jul/25 $$\mathrm{find}\:{y} \\ $$$${y}^{{dy}} =\:{x}^{{dx}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 223055 by alcohol last updated on 13/Jul/25 Commented by alcohol last updated on 13/Jul/25 $${please}\:{i}\:{really}\:{really}\:{need}\:{a}\:{detailed} \\ $$$${explanation} \\ $$ Commented by mr W…
Question Number 223049 by wewji12 last updated on 13/Jul/25 $$\mathrm{we}\:\mathrm{already}\:\mathrm{know}\:\:\underset{{h}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{h}}=\infty\:\mathrm{and}\:\underset{{p}\in\mathbb{P}} {\sum}\:\frac{\mathrm{1}}{{p}}=\infty \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{Harmonic}\:\mathrm{Series} \\ $$$$\underset{{h}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{h}}=\underset{{p}\in\mathbb{P}} {\prod}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{p}}+\left(\frac{\mathrm{1}}{{p}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{{p}}\right)^{\mathrm{3}} +…\right)=\:\underset{{p}\in\mathbb{P}} {\prod}\:\frac{\mathrm{1}}{\mathrm{1}−{p}^{−\mathrm{1}} } \\…
Question Number 223044 by hardmath last updated on 13/Jul/25 Commented by hardmath last updated on 13/Jul/25 $$ \\ $$Find the voltmeter reading in the electrical…
Question Number 223040 by MrGaster last updated on 13/Jul/25 Commented by Nicholas666 last updated on 14/Jul/25 $$\:\:\mathrm{thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{sir},\: \\ $$$$\:\mathrm{very}\:\mathrm{nice}\:\mathrm{you}'\mathrm{re}\:\mathrm{approach}\:\:\:\mathrm{solution}\:\mathrm{to}\:\mathrm{this}\:\mathrm{problem}\: \\ $$$$ \\ $$ Terms of…
Question Number 223042 by Tawa11 last updated on 13/Jul/25 Commented by Tawa11 last updated on 13/Jul/25 $$\mathrm{Is}\:\:\mathrm{x}\:\:=\:\:\mathrm{5}.\mathrm{139}°\:\:\mathrm{or}\:\:\mathrm{x}\:\:=\:\:\mathrm{80}° \\ $$ Commented by mr W last updated…
Question Number 223006 by mnjuly1970 last updated on 12/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\mathscr{L}\:\:\left\{\:{tsin}\left(\sqrt{{t}}\:\right)\right\}=? \\ $$ Answered by MrGaster last updated on 12/Jul/25 $$\mathscr{L}\:\:\left\{\:{tsin}\left(\sqrt{{t}}\:\right)\right\}=\int_{\mathrm{0}} ^{\infty} {e}^{−{st}} {t}\:\mathrm{sin}\left(\sqrt{{t}}\right){dt}…
Question Number 222974 by gabthemathguy25 last updated on 12/Jul/25 Answered by MrGaster last updated on 12/Jul/25 $${P}_{\mathrm{100}} =\mathrm{min}\left\{{x}\in\mathbb{N}\mid\underset{{k}=\mathrm{1}} {\overset{{x}} {\sum}}\underset{{i}=\mathrm{2}} {\overset{\lfloor\sqrt{{k}}\rfloor} {\prod}}\left(\mathrm{1}−\delta\left({k}\:\mathrm{mod}\:{i}\right)\right)\geq\mathrm{101}\right\} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{540}}…
Question Number 223007 by Nicholas666 last updated on 12/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\mathrm{everyone}\:\mathrm{or}\:\mathrm{Mr}.\:\mathrm{Gaster}\:! \\ $$$$\:\:\:\:\:\:\:\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{how}\:\mathrm{to}\:\mathrm{sove}\:\mathrm{the}\:\mathrm{integral}\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{Because}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{is}\:\mathrm{very}\:\mathrm{crazy}\:\mathrm{or}\:\mathrm{very}\:\mathrm{Complicated} \\ $$$$\:\:\:\:\:\:\mathrm{Problem}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{ln}\left({x}−\mathrm{1}\right)\:\mathrm{ln}\left({x}+\mathrm{1}\right)\:\mathrm{ln}\:\left({x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\:\mathrm{d}{x}\:=??? \\…