Category: Integration

Question Number 36187 by prof Abdo imad last updated on 30/May/18 $$let{I}_n\left(x\right)={\int }_0^{\mathrm{\infty }}\frac{tsin\left(t\right)}{{(t^2+x^2)}^n}dt$$$$1)findarelationbetween{I}_{n+1}and{I}_n$$$$\left.\mathrm{2}\right)\:{calculate}\:{I}_{\mathrm{2}} \left({x}\right)\:{and}\:{I}_{\mathrm{3}} \left({x}\right)\:…

Question Number 36185 by prof Abdo imad last updated on 30/May/18 $$studythevonvergenceof$$$${\int }_1^{+\mathrm{\infty }}\frac{e^{-\frac{1}{t}}-cos\left(\frac{1}{t}\right)}{t}dt$$ Commented by maxmathsup by imad last…

Question Number 36180 by prof Abdo imad last updated on 30/May/18 $$calculate{\int }_0^1\frac{ln\left(t\right)}{{(1+t)}^2}dt$$ Commented by prof Abdo imad last updated on…

Question Number 36182 by prof Abdo imad last updated on 30/May/18 $$calculate{\int }_1^{+\mathrm{\infty }}\frac{dt}{t\sqrt{1+t^2}}$$ Commented by maxmathsup by imad last updated on…

Question Number 167223 by cortano1 last updated on 10/Mar/22 $$\int \sin {}^3\left(3\mathrm{x}\right)\cos {}^4\left(5\mathrm{x}\right)\mathrm{dx}=?$$ Commented by greogoury55 last updated on 10/Mar/22 $$\sin {}^3\left(3x\right)=\frac{3\sin \left(3x\right)-\sin \left(9x\right)}{4}$$$$\:\mathrm{cos}\:^{\mathrm{4}}…