Category: Integration

Question Number 122734 by bemath last updated on 19/Nov/20 Answered by liberty last updated on 19/Nov/20 $$Justapplyingpartialfaction$$$$\:\frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{6}{x}−\mathrm{4}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}\right)}\:=\:\frac{{Ax}+{B}}{{x}^{\mathrm{2}} +\mathrm{1}}+\:\frac{{Cx}+{D}}{{x}^{\mathrm{2}} +\mathrm{2}}…

Question Number 122713 by mnjuly1970 last updated on 19/Nov/20 $$\dots advancedmath\dots$$$$twosimpleandniceintegrals:$$$$provethat::$$$${\mathrm{\Omega }}_1={\int }_0^{\mathrm{\infty }}\frac{sin\left(e^{-\gamma }x\right)ln\left(x\right)}{x}dx=0$$$$\:\:\:\:\:\:\:\:\:\:\:\:\Omega_{\mathrm{2}} \:=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}^{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}}…

Question Number 122689 by john santu last updated on 19/Nov/20 $$Evaluatetheintegral$$$$\int \frac{\sqrt[3]{x}+1}{\sqrt[3]{x}-1}dx$$ Answered by bobhans last updated on 19/Nov/20 $$\:{let}\:{x}\:=\:{u}^{\mathrm{3}} \:\Rightarrow{dx}\:=\:\mathrm{3}{u}^{\mathrm{2}} \:{du}\:…

Question Number 188192 by universe last updated on 26/Feb/23 $$$$$$provethat$$$${\int }_0^{\mathrm{\infty }}{e}^{-a^2{x}^2}\cos \left(2bx\right)dx=\frac{\sqrt{\pi }}{2a}{e}^{-b^2/a^2}$$$$$$$$…

Question Number 57103 by turbo msup by abdo last updated on 30/Mar/19 $$let{A}_n=\int {\int }_{w_n}{e}^{-x^2-y^2}\sqrt{x^2+y^2}dxdy$$$${with}\:{w}_{{n}} =\left[\frac{\mathrm{1}}{{n}},{n}\right]×\left[\frac{\mathrm{1}}{{n}},{n}\right] \…