Question Number 222413 by Shrodinger last updated on 25/Jun/25 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{xsinxcosx}}{{tan}^{\mathrm{2}} {x}+{cotan}^{\mathrm{2}} {x}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222415 by Tawa11 last updated on 25/Jun/25 Answered by MrGaster last updated on 26/Jun/25 $${t}=\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{2}−{x}}} \\ $$$${x}=\frac{\mathrm{1}−\mathrm{2}{t}^{\mathrm{2}} }{\mathrm{1}−{t}^{\mathrm{2}} } \\ $$$${dx}=\frac{−\mathrm{2}{t}}{\left(\mathrm{1}−{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dt}…
Question Number 222408 by Nicholas666 last updated on 25/Jun/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{1}} ^{\infty} \:\left(\frac{\mathrm{1}}{{x}}\right)^{\frac{{x}}{\:\sqrt{{x}−\mathrm{1}}}} \:{dx}\:=\:\:\:?? \\ $$$$ \\ $$ Answered by MrGaster last updated on…
Question Number 222409 by Nicholas666 last updated on 25/Jun/25 $$ \\ $$$$\:\:\:\mathrm{Solve}\:;\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{ln}^{{n}} \:\mathrm{sin}\:\theta}{\mathrm{sin}^{{p}} \:\theta\:\mathrm{cos}^{{q}} \:\theta}\:\mathrm{d}\theta\:,\:\mathrm{for}\:{n},{p},{q}\:\in\:\mathbb{R}_{\geqslant\:\mathrm{0}} \:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service…
Question Number 222411 by Nicholas666 last updated on 25/Jun/25 $$\:\: \\ $$$$\:\:\:\left[\:\mathrm{1}\:.\right]\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}\left({x}\right)\:\mathrm{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}−{x}^{\mathrm{2}} }\:\:\:{dx}\:\:\:\:\: \\ $$$$\:\:\:\left[\:\mathrm{2}\:.\right]\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\mathrm{ln}\left({x}\right)\:\mathrm{ln}\left(\mathrm{1}−{x}\right)\:\mathrm{ln}\left(\mathrm{1}+{x}\right)\:\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}}\:{dx} \\ $$$$\:\left[\:\mathrm{3}\:.\right]\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 222331 by Nicholas666 last updated on 22/Jun/25 $$ \\ $$$$\:\:\:\:\:\:\:\mathrm{Find}\:\mathrm{closed}\:\mathrm{form}; \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{Li}_{\mathrm{2}} \left({z}^{\mathrm{2}} \right)\mathrm{Li}_{\mathrm{2}} \left(−{z}^{\mathrm{2}} \right)}{\mathrm{1}\:+\:{z}^{\mathrm{2}} }\:\mathrm{d}{z}\:=\:? \\ $$ Terms of…
Question Number 222292 by Nicholas666 last updated on 22/Jun/25 $$ \\ $$$$\:\:\:\int_{−\infty} ^{\infty} \mathrm{sech}\left({z}\right)\:\mathrm{sech}\left({z}−{a}\right)\:{dz} \\ $$$$ \\ $$ Answered by Frix last updated on 22/Jun/25…
Question Number 222295 by alvan545 last updated on 22/Jun/25 Answered by MrGaster last updated on 22/Jun/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222336 by Nicholas666 last updated on 22/Jun/25 $$ \\ $$$$\:\:\:\:\:\:\:\int\int\int\:\:\frac{−{y}\:\pm\:\sqrt{{y}^{\mathrm{2}} \:+\:\mathrm{4}{xy}}}{\mathrm{2}{x}}\:{dxdydz} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222285 by Shrodinger last updated on 21/Jun/25 $$\int\frac{{x}^{\mathrm{5}} −{x}^{\mathrm{3}} +\mathrm{2}{x}+\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}\:{e}^{−\frac{\mathrm{1}}{\mathrm{4}}{ln}\left({x}^{\mathrm{4}} +\mathrm{1}\right)} {dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com