Category: Integration

Question Number 56935 by maxmathsup by imad last updated on 27/Mar/19 $$1.calculate{U}_n={\int }_0^{\mathrm{\infty }}(x^3-2x+1)e^{-n\left[x\right]}dxwithnintegrnaturalandn⩾1$$$$2.findnatureof\mathrm{\Sigma }{U}_n$$ Commented by maxmathsup by…

Question Number 56931 by turbo msup by abdo last updated on 26/Mar/19 $$calculate{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{x^2-1}{{(x^2-x+3)}^2}dx$$ Commented by maxmathsup by imad…

Question Number 122461 by benjo_mathlover last updated on 17/Nov/20 $$\int \frac{x}{(x^2+a^2)(x^3+b^2)}?$$ Commented by liberty last updated on 17/Nov/20 $$\mathrm{Ostrogradsky}..\mathrm{method}.\: \…

Question Number 122430 by benjo_mathlover last updated on 17/Nov/20 $$\int \frac{x^3}{\sqrt{4-x^2}+x^2-4}dx$$ Answered by liberty last updated on 17/Nov/20 $$\:\mathrm{let}\:\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }\:=\:\omega\:\wedge\:\mathrm{x}^{\mathrm{2}} −\mathrm{4}\:=−\omega^{\mathrm{2}}…

Question Number 122366 by rs4089 last updated on 16/Nov/20 Answered by mathmax by abdo last updated on 16/Nov/20 $$\mathrm{I}={\int }_0^{\mathrm{\infty }}\frac{\sin \left(\mathrm{sinx}\right)}{\mathrm{x}}{\mathrm{e}}^{\mathrm{cosx}}\mathrm{dx}\mathrm{the}\mathrm{function}\mathrm{under}\mathrm{integral}\mathrm{is}\mathrm{even}\Rightarrow$$$$\mathrm{2I}=\int_{−\infty} ^{+\infty}…