Question Number 88902 by M±th+et£s last updated on 13/Apr/20 $$\int_{\frac{\mathrm{1}}{{e}}} ^{{e}} {ln}\mid{x}\mid\:{dx} \\ $$ Commented by abdomathmax last updated on 13/Apr/20 $$\int_{\frac{\mathrm{1}}{{e}}} ^{{e}} \:{ln}\mid{x}\mid{dx}\:=\left[{xlnx}−{x}\right]_{\frac{\mathrm{1}}{{e}}} ^{{e}}…
Question Number 154421 by peter frank last updated on 18/Sep/21 $$\int\left[\left(\frac{\mathrm{x}}{\mathrm{e}}\right)^{\mathrm{x}} +\left(\frac{\mathrm{e}}{\mathrm{x}}\right)^{\mathrm{x}} \right]\mathrm{ln}\:\mathrm{xdx} \\ $$ Answered by puissant last updated on 18/Sep/21 $${Q}=\int\left[\left(\frac{{x}}{{e}}\right)^{{x}} +\left(\frac{{e}}{{x}}\right)^{{x}} \right]{lnx}\:{dx}\:…
Question Number 154422 by peter frank last updated on 18/Sep/21 $$\int\frac{\mathrm{a}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \theta+\mathrm{b}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \theta}{\mathrm{a}^{\mathrm{4}} \mathrm{sin}\:^{\mathrm{2}} \theta+\mathrm{b}^{\mathrm{4}} \mathrm{cos}\:^{\mathrm{2}} \theta}\mathrm{d}\theta \\ $$ Terms of Service Privacy…
Question Number 154409 by mnjuly1970 last updated on 18/Sep/21 $$ \\ $$$$\:\:{nice}\:{calculus}.. \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$\: \\ $$$$\:\mathrm{I}:=\int_{\mathrm{0}} ^{\:\infty} \frac{\:\left(\mathrm{1}+{e}^{\:−{x}} \:\right){sin}^{\:\mathrm{2}} \left({x}\right)}{{x}^{\:\frac{\mathrm{3}}{\mathrm{2}}} }\:=\sqrt{\mathrm{2}\pi}\:\left(\:\mathrm{1}+\:\sqrt{\sqrt{\mathrm{2}}\:−\:\mathrm{1}}\:\right) \\ $$$$\:{m}.{n}…
Question Number 88863 by M±th+et£s last updated on 13/Apr/20 $$\int\frac{\mathrm{8}{cos}^{\mathrm{3}} \left({x}\right)}{\mathrm{8}+{sin}^{\mathrm{3}} \mathrm{2}{x}}{dx} \\ $$$$ \\ $$ Commented by MJS last updated on 13/Apr/20 $$\mathrm{I}\:\mathrm{tried}\:\mathrm{everything}\:\mathrm{I}\:\mathrm{know},\:\mathrm{seems}\:\mathrm{impossible} \\…
Question Number 88859 by 242242864 last updated on 13/Apr/20 $$\int\:\boldsymbol{{e}}^{\boldsymbol{{ax}}} \mathrm{cos}\:\boldsymbol{{bx}}\:\boldsymbol{{dx}} \\ $$$$\int\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{e}}^{\mathrm{2}\boldsymbol{{x}}} \boldsymbol{{ln}}\mathrm{3}\boldsymbol{{x}}^{\mathrm{2}} \:\boldsymbol{{dx}} \\ $$ Commented by john santu last updated on…
Question Number 88852 by M±th+et£s last updated on 13/Apr/20 $${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{{n}} \lceil{x}\rceil{dx}=\:\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}\:{and}\:\int_{\mathrm{0}} ^{{n}} \lfloor{x}\rfloor{dx}=\frac{{n}\left({n}−\mathrm{1}\right)}{\mathrm{2}} \\ $$$${when}\:\lfloor..\rfloor\:{is}\:{floor}\:{and}\:\lceil..\rceil\:{is}\:{ceil} \\ $$ Answered by mr W last…
Question Number 23283 by ajfour last updated on 28/Oct/17 $${Compute}\:{the}\:{area}\:{of}\:{a}\:{loop}\:{of} \\ $$$${the}\:{curve}\:\boldsymbol{\rho}=\boldsymbol{{a}}\mathrm{sin}\:\mathrm{2}\boldsymbol{\theta}\:;\:{and}\:{even} \\ $$$${sketch}\:{the}\:{curve},\:{please}. \\ $$ Answered by mrW1 last updated on 28/Oct/17 $$\mathrm{a}\:\mathrm{small}\:\mathrm{loop}\:\mathrm{for}\:\theta\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\frac{\pi}{\mathrm{2}}: \\…
Question Number 154352 by amin96 last updated on 17/Sep/21 $$\:\int\frac{{x}^{{n}−\mathrm{1}} }{{x}^{\mathrm{3}{n}+\mathrm{1}} \left({x}^{{n}} −\mathrm{1}\right)}{dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 88789 by M±th+et£s last updated on 12/Apr/20 $$\int\int{ln}\left({x}+\mathrm{1}\right)\:{dx}\:{dy} \\ $$ Commented by mr W last updated on 13/Apr/20 $$\int\:\mathrm{ln}\left(\mathrm{x}+\mathrm{1}\right)\:\mathrm{dx}\:=\:\int\:\mathrm{ln}\:\mathrm{u}\:\mathrm{du} \\ $$$$….. \\ $$$$=\:\left({x}+\mathrm{1}\right)\:\mathrm{ln}\left({x}+\mathrm{1}\right)−\left({x}+\mathrm{1}\right)+{c}\left({y}\right)…