Question Number 94184 by MJS last updated on 17/May/20 $$\int\frac{{x}\sqrt[{\mathrm{3}}]{{x}−{a}}}{\:\sqrt[{\mathrm{3}}]{{x}−{b}}}{dx}=? \\ $$$$\int\frac{\sqrt[{\mathrm{3}}]{{x}−{a}}}{{x}\sqrt[{\mathrm{3}}]{{x}−{b}}}{dx}=? \\ $$ Commented by MJS last updated on 17/May/20 I can solve both but I want to know if there's an easier path. will post my solutions later. Answered by M±th+et+s…
Question Number 159717 by cortano last updated on 20/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 94161 by i jagooll last updated on 17/May/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{p}+\sqrt{\mathrm{qx}+\mathrm{r}}}\: \\ $$ Commented by mathmax by abdo last updated on 17/May/20 $${I}\:=\int\:\:\frac{{dx}}{{p}+\sqrt{{qx}+{r}}}\:\:{we}\:{use}\:{the}\:{changememt}\:\sqrt{{qx}+{r}}={t}\:\Rightarrow \\ $$$${qx}+{r}\:={t}^{\mathrm{2}}…
Question Number 159693 by mnjuly1970 last updated on 20/Nov/21 $$ \\ $$$$\:\:\:\:\:\:\:\Omega:=\int_{\mathrm{1}} ^{\:\mathrm{10}} {x}\:{d}\:\left({x}\:+\:\lfloor\:{x}\:\rfloor\right)\:=? \\ $$$$ \\ $$ Answered by mr W last updated on…
Question Number 28615 by abdo imad last updated on 27/Jan/18 $${find}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{shx}}{{x}}\:{e}^{−\mathrm{3}{x}} {dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28613 by abdo imad last updated on 27/Jan/18 $${let}\:{give}\:{x}>\mathrm{0}\:\:{and}\:{S}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{sint}}{{e}^{{xt}} −\mathrm{1}}{dt}\:. \\ $$$${developp}\:{S}\:{at}\:{form}\:{of}\:{series}. \\ $$ Commented by abdo imad last updated on…
Question Number 159681 by mnjuly1970 last updated on 20/Nov/21 $$ \\ $$$$\:\:\:\:{prove}\:{that}\:: \\ $$$$\mathrm{P}=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}\left({n}+\mathrm{2}\right)}\:\right)\:\overset{?} {=}\:\frac{−\sqrt{\mathrm{2}}\:{sin}\left(\pi\sqrt{\mathrm{2}}\:\right)}{\pi} \\ $$$$\:\:\:\:\:{m}.{n} \\ $$ Answered by mindispower last…
Question Number 159680 by cortano last updated on 20/Nov/21 $$\:\:\:\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{6}}} \:\frac{\mathrm{sin}\:{x}\:\mathrm{sin}\:\left({x}+\mathrm{60}°\right)\:\mathrm{sin}\:\left({x}+\mathrm{120}°\right)}{\mathrm{cos}\:\mathrm{3}{x}\:+\:\mathrm{sin}\:\mathrm{3}{x}}\:{dx}=? \\ $$ Commented by cortano last updated on 20/Nov/21 $$\:{let}\:\theta=\mathrm{3}{x}\:\Rightarrow{I}=\frac{\mathrm{1}}{\mathrm{12}}\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{sin}\:\:\theta}{\mathrm{cos}\:\theta+\mathrm{sin}\:\theta}\:{d}\theta \\…
Question Number 28611 by abdo imad last updated on 27/Jan/18 $$\left.{let}\:{give}\:\theta\in\right]\mathrm{0},\pi\left[\:\:{prove}\:{that}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{{e}^{−{i}\theta} −{t}}=\:\sum_{{n}=\mathrm{1}} ^{+\infty} \:\:\frac{{e}^{{in}\theta} }{{n}}\:\:.\right. \\ $$ Commented by abdo imad last updated…
Question Number 28610 by abdo imad last updated on 27/Jan/18 $${let}\:{give}\:{I}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{dt}}{\:\sqrt{{sin}^{\mathrm{2}} {t}\:+{x}^{\mathrm{2}} \:{cos}^{\mathrm{2}} {t}}}\:\:{and} \\ $$$${J}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{cost}}{\:\sqrt{{sin}^{\mathrm{2}} {t}\:+{x}^{\mathrm{2}} {cos}^{\mathrm{2}} {t}}}{dt}\:{cslculate}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \left({I}\left({x}\right)−{J}\left({x}\right)\right)…