Question Number 215540 by MrGaster last updated on 10/Jan/25 $$\int_{\underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{x}_{{i}} ^{\mathrm{2}} \leq\mathrm{1}} \left(\underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{x}_{{i}} ^{\mathrm{2}} \right)^{{m}} \left(\underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{a}_{{i}} {x}_{{i}} \right)^{\mathrm{2}{k}} \underset{\mathrm{1}\leq{i}\leq{n}} {\prod}{dx}_{{i}} \\ $$…
Question Number 215535 by MrGaster last updated on 10/Jan/25 $$\int_{\underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{x}_{{i}} ^{\mathrm{2}} \leq{R}^{\mathrm{2}} } \underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{x}_{{i}} \frac{\partial{f}}{\partial{x}_{{i}} }\underset{\mathrm{1}\leq{i}\leq{n}} {\prod}{dx}_{{i}} =? \\ $$ Answered by MrGaster…
Question Number 215496 by MATHEMATICSAM last updated on 08/Jan/25 $$\int_{\mathrm{0}} ^{\pi} \frac{{x}\mathrm{tan}{x}}{\mathrm{sec}{x}\:+\:\mathrm{tan}{x}}\:{dx} \\ $$$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{integral}. \\ $$ Commented by mr W last updated on 09/Jan/25 $$=\frac{\pi^{\mathrm{2}}…
Question Number 215498 by alephnull last updated on 08/Jan/25 $$\int\left({e}^{−\omega{u}} +\mathrm{cos}\left({u}\right)−\frac{\mathrm{sin}\left(\omega{u}\right)}{{e}^{{u}} }\right){du} \\ $$ Answered by MathematicalUser2357 last updated on 10/Jan/25 $$−\frac{{e}^{−{u}\omega} }{\omega}+\frac{{e}^{−{u}} \mathrm{sin}\:{u}\omega}{\left(\omega−{i}\right)\left(\omega+{i}\right)}+\frac{{e}^{−{u}} \omega\mathrm{cos}\:{u}\omega}{\left(\omega−{i}\right)\left(\omega+{i}\right)}+\mathrm{sin}\:{u}+{C}…
Question Number 215458 by depressiveshrek last updated on 07/Jan/25 $$\mathrm{Evaluate}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}^{\mathrm{2}} \:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}+\mathrm{1}} \mathrm{sin}\left(\pi{x}\right){dx} \\ $$ Answered by MathematicalUser2357 last updated on 11/Jan/25 $$\underset{{n}\rightarrow\infty}…
Question Number 215414 by MATHEMATICSAM last updated on 06/Jan/25 $$\int\:\frac{\mathrm{sin}^{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}}\right)\mathrm{sec}\left(\frac{{x}}{\mathrm{2}}\right)}{\:\sqrt{\mathrm{cos}^{\mathrm{3}} {x}\:+\:\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{cos}{x}}}\:{dx} \\ $$$$\mathrm{Solve}\:\mathrm{this}\:\mathrm{integral}. \\ $$ Commented by JamesZhou last updated on 06/Jan/25 $${maybe}\:{numerator}\:{issi}\hat…
Question Number 215434 by ajfour last updated on 06/Jan/25 $$\int_{\mathrm{0}} ^{\:\:{t}} \sqrt{\frac{{t}}{{b}−{t}}}\:{e}^{{t}} {dt}\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 215404 by ajfour last updated on 05/Jan/25 $$\int_{{a}} ^{\:\:{x}} \:\frac{\sqrt{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }}{\:\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }}{dx}\:=\:? \\ $$ Answered by Ghisom last updated on 06/Jan/25 $$\int\frac{\sqrt{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}}…
Question Number 215390 by MathematicalUser2357 last updated on 05/Jan/25 $$\oint_{\gamma} {x}^{\mathrm{2}} {dx}\:\left[\gamma:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\right] \\ $$ Answered by MrGaster last updated on 05/Jan/25 $$\mathrm{solve}:\int_{\mathrm{0}} ^{\mathrm{2}\pi}…
Question Number 215393 by MrGaster last updated on 05/Jan/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{2}\nu} }{\left({x}^{\mathrm{2}} +\beta^{\mathrm{2}} \right)^{\mu+\mathrm{1}} }\mathrm{sin}\left({ax}\right){dx} \\ $$$$ \\ $$ Commented by JamesZhou…