Question Number 29506 by abdo imad last updated on 09/Feb/18 $${le}\:{give}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{sin}\left(\left(\mathrm{2}{n}−\mathrm{1}\right){x}\right)}{{sinx}}{dx}\:{and}\:{B}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{sin}^{\mathrm{2}} \left({nx}\right)}{{sin}^{\mathrm{2}} {x}}{dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{B}_{{n}+\mathrm{1}} −{B}_{{n}} =\:{A}_{{n}+\mathrm{1}}…
Question Number 160563 by qaz last updated on 02/Dec/21 $$\int\mathrm{x}\left\{\mathrm{x}\right\}\left[\mathrm{x}\right]\mathrm{dx}=? \\ $$ Answered by mr W last updated on 02/Dec/21 $$\left[{x}\right]={n} \\ $$$$\left\{{x}\right\}={x}−{n} \\ $$$$\int{x}\left\{{x}\right\}\left[{x}\right]{dx}…
Question Number 160556 by amin96 last updated on 01/Dec/21 $$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{arctg}}\left(\boldsymbol{\mathrm{x}}\right)}{\mathrm{1}+\boldsymbol{\mathrm{x}}}\centerdot\frac{\boldsymbol{\mathrm{dx}}}{\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{x}}}}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 95012 by M±th+et+s last updated on 22/May/20 $$\int\frac{\mathrm{1}}{\:\sqrt{\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left({x}−\mathrm{3}\right)\left({x}−\mathrm{4}\right)}}{dx} \\ $$ Commented by mathmax by abdo last updated on 23/May/20 $$\mathrm{its}\:\mathrm{seems}\:\mathrm{that}\:\mathrm{integral}\:\mathrm{is}\:\mathrm{elliptic} \\ $$ Terms…
Question Number 160551 by qaz last updated on 01/Dec/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{arctan}\:\mathrm{x}\centerdot\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)\mathrm{dx}=? \\ $$ Commented by smallEinstein last updated on 07/Jan/22 Commented by smallEinstein last…
Question Number 160547 by mnjuly1970 last updated on 01/Dec/21 $$\:\:{solve} \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{\:{tan}^{\:−\mathrm{1}} \left(\:{x}\:\right)}{\left(\mathrm{1}+\:{x}^{\:\mathrm{2}} \:\right)\sqrt{\:{x}}}\:{dx}=\:? \\ $$$$−−−−−−−− \\ $$ Answered by Kamel last updated…
Question Number 160543 by mnjuly1970 last updated on 01/Dec/21 $$ \\ $$$$\mathrm{lim}_{\:{x}\rightarrow\:\mathrm{6}} \frac{\:\Gamma\:\left(\:{sin}\left(\:\frac{\pi}{{x}}\right)\right)−\Gamma\:\left(\frac{\mathrm{3}}{{x}}\:\right)}{{sin}\left(\:\pi{x}\:\right)}=\:? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 95009 by bobhans last updated on 22/May/20 $$\int\:\:\frac{{e}^{{x}} +\mathrm{2}{xe}^{{x}} \mathrm{sin}\:{x}−\mathrm{2}{xe}^{{x}} \mathrm{cos}\:{x}}{\:\sqrt{{x}}\:\mathrm{sin}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$ Commented by bobhans last updated on 22/May/20 my children exam Commented…
Question Number 29455 by prof Abdo imad last updated on 08/Feb/18 $${find}\:\int\:\:\mathrm{3}^{\sqrt{\mathrm{2}{x}+\mathrm{1}}} \:{dx}\:. \\ $$ Commented by prof Abdo imad last updated on 12/Feb/18 $${the}\:{ch}.\:\sqrt{\mathrm{2}{x}+\mathrm{1}}\:={t}\:{give}\:\mathrm{2}{x}+\mathrm{1}={t}^{\mathrm{2}}…
Question Number 29454 by prof Abdo imad last updated on 08/Feb/18 $${f}\:{is}\:{a}\:{function}\:{increasing}\:{and}\:{C}^{\mathrm{1}} {on}\:\left[{a},{b}\right]\:{prove} \\ $$$$\:\int_{{f}\left({a}\right)} ^{{f}\left({b}\right)} \:{f}^{−\mathrm{1}} \left({t}\right){dt}\:=\:\int_{{a}} ^{{b}} \:{x}\:{f}^{'} \left({x}\right){dx}\: \\ $$ Commented by…