Category: Integration

Question Number 59800 by necx1 last updated on 14/May/19 $$findthegeneralsolutiony\left(t\right)ofthe$$$$ordinarydifferentialequation$$$$y^{″}+{\omega }^{2}y=\cos \omega t,wherew>0$$ Answered by MJS last updated on 15/May/19 $$\mathrm{1}^{\mathrm{st}}…

Question Number 190841 by Rupesh123 last updated on 12/Apr/23 Answered by ARUNG_Brandon_MBU last updated on 12/Apr/23 $$I={\int }_0^{\pi }\frac{xdx}{1+\cos \alpha \sin x}={\int }_0^{\pi }\frac{\pi -x}{1+\cos \alpha \sin x}dx$$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\pi} \frac{\pi}{\mathrm{1}+\mathrm{cos}\alpha\mathrm{sin}{x}}{dx}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}}…

Question Number 125276 by Study last updated on 09/Dec/20 $$\underset{0}{\stackrel{1}{\int }}\frac{x^9-1}{lnx}dx=???$$ Answered by Dwaipayan Shikari last updated on 09/Dec/20 $${I}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 59732 by maxmathsup by imad last updated on 14/May/19 $$find{I}_n=\int \frac{dx}{{sin}^{n}x}withnintegrnatural.$$ Answered by tanmay last updated on 14/May/19 $${I}_{{n}} =\int{cosec}^{{n}}…

Question Number 125233 by mathmax by abdo last updated on 09/Dec/20 $$\mathrm{calculate}{\mathrm{u}}_{\mathrm{nm}}={\int }_0^{\mathrm{\infty }}{\mathrm{e}}^{-\mathrm{nx}}\ln (1+{\mathrm{e}}^{\mathrm{mx}})\mathrm{dx}$$$$\mathrm{find}\sum _{\mathrm{n}⩾0\mathrm{and}\mathrm{m}⩾0}{\mathrm{u}}_{\mathrm{nm}}$$ Terms of Service…