Category: Integration

Question Number 70872 by Abdo msup. last updated on 09/Oct/19 $$calculate\int {\int }_{{[1,3]}^2}{e}^{-x-y}ln(2x+y)dxdy$$ Commented by Abdo msup. last updated on 11/Oct/19 $${let}\:{I}=\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}}…

Question Number 70870 by Abdo msup. last updated on 09/Oct/19 $$letf\left(x\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{dt}{{(t^2-2t+x^2)}^4}with\mid x\mid >1$$$$andnintegrnatural$$$$1)findaexplicitformforf\left(x\right)$$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+{x}^{\mathrm{2}}…

Question Number 70871 by Abdo msup. last updated on 09/Oct/19 $$calculatef\left(x\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{cos\left(x(1+t^2)\right)}{1+t^2}dtwithx⩾0$$ Commented by mathmax by abdo last updated on…

Question Number 136401 by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{find}{\int }_0^{\mathrm{\infty }}\frac{\arctan \left({\mathrm{x}}^2\right)}{{\mathrm{x}}^4+1}\mathrm{dx}$$ Answered by Dwaipayan Shikari last updated on…

Question Number 136402 by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{find}{\mathrm{U}}_{\mathrm{n}}={\int }_{\frac{1}{\mathrm{n}}}^{\mathrm{n}}(1-\frac{1}{{\mathrm{x}}^2})\arctan (\mathrm{x}+\frac{1}{\mathrm{x}})\mathrm{dx}$$$$\mathrm{and}{\lim }_{\mathrm{n}\to \mathrm{\infty }}{\mathrm{U}}_{\mathrm{n}}$$ Terms of Service Privacy…