Category: Integration

Question Number 33736 by prof Abdo imad last updated on 23/Apr/18 $$findthevalueof{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{x^2}{{(1+x+x^2)}^2}dx$$ Commented by prof Abdo imad last…

Question Number 99261 by Ar Brandon last updated on 19/Jun/20 $$\mathrm{Given}\mathrm{F}\left(\mathrm{x}\right)=\frac{1}{2}\int \frac{\mathrm{x}+1}{\mathrm{x}-1}\mathrm{f}\left(\mathrm{t}\right)\mathrm{dt}$$$$\mathrm{Show}\mathrm{that}\mathrm{F}\mathrm{is}\mathrm{defined},\mathrm{continuous},\mathrm{and}\mathrm{derivable}.$$$$\mathrm{And}\mathrm{find}\mathrm{its}\mathrm{derivative}$$ Answered by abdomathmax last updated on 19/Jun/20 $$\mathrm{F}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}}{\mathrm{2}}\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\:\int^{\mathrm{x}}…

Question Number 33703 by math khazana by abdo last updated on 22/Apr/18 $$give{\int }_0^{\mathrm{\infty }}\frac{x{e}^{-x}}{1-e^{-2x}}sin\left(\pi x\right)dxatformofserie.$$ Terms of Service Privacy Policy Contact:…

Question Number 99239 by abdomathmax last updated on 19/Jun/20 $$\mathrm{calculate}{\int }_2^{+\mathrm{\infty }}\frac{\mathrm{dx}}{{\mathrm{x}}^3{({\mathrm{x}}^2-1)}^2}$$ Answered by MJS last updated on 19/Jun/20 $$\mathrm{Ostrogradski}\:\mathrm{gives}…

Question Number 33695 by math khazana by abdo last updated on 22/Apr/18 $$find{lim}_{n\to +\mathrm{\infty }}{\int }_0^{\mathrm{\infty }}\frac{e^{-\frac{x}{n}}}{1+x^2}dx.$$ Commented by math khazana by…