Menu Close

Category: Integration

1-i-n-x-i-2-1-1-i-n-x-i-2-m-1-i-n-a-i-x-i-2k-1-i-n-dx-i-

Question Number 215540 by MrGaster last updated on 10/Jan/25 $$\int_{\underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{x}_{{i}} ^{\mathrm{2}} \leq\mathrm{1}} \left(\underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{x}_{{i}} ^{\mathrm{2}} \right)^{{m}} \left(\underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{a}_{{i}} {x}_{{i}} \right)^{\mathrm{2}{k}} \underset{\mathrm{1}\leq{i}\leq{n}} {\prod}{dx}_{{i}} \\ $$…

e-u-cos-u-sin-u-e-u-du-

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}…

sin-3-x-2-sec-x-2-cos-3-x-cos-2-x-cosx-dx-Solve-this-integral-

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…