Category: Integration

Question Number 25769 by abdo imad last updated on 14/Dec/17 $${a}−{nser}\:{to}\:{question}\:\mathrm{25765}…{we}\:{put}\:{I}=\int_{\mathrm{0}} ^{\infty} \left({cos}\left({x}^{\mathrm{2}{n}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{−\mathrm{1}} {dx}\:{and}\:{J}=\int_{\mathrm{0}} ^{\infty} {sin}\left({x}^{\mathrm{2}{n}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{−\mathrm{1}} {dx}…{we}\:{have}\:\mathrm{2}\left({I}+{iJ}\right)=\int_{{R}} {e}^{{ix}^{\mathrm{2}{n}} } \left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{−\mathrm{1}}…

Question Number 25762 by abdo imad last updated on 14/Dec/17 $$findthevalueof{\int }_0^{\mathrm{\infty }}artan\left(2x\right){(1+x^2)}^{-1_{}}thekeyofslutionputF\left(t\right)={\int }_0^{\mathrm{\infty }}artan\left(xt\right){(1+x^2)}^{-1}find\partial F/\partial tfirstthenF\left(t\right)andtaket=2youwilloffindfindthevalueofintegral..$$ Terms of Service…

Question Number 91271 by mathmax by abdo last updated on 29/Apr/20 $$calculate{\int }_0^1\frac{ln(1+x)}{{(x+1)}^2}dx$$ Commented by mathmax by abdo last updated on…

Question Number 91269 by mathmax by abdo last updated on 29/Apr/20 $$calculate{\int }_0^{\mathrm{\infty }}\frac{x^2-1}{{(x^2+x+2)}^3}dx$$ Terms of Service Privacy Policy Contact:…

Question Number 156775 by mnjuly1970 last updated on 15/Oct/21 $$$$$$fisafunctionthatassigns$$$$toeachnaturalnumber$$$$multiplicationofitsdigits$$$$forexampl:f\left(200\right)=0$$$$f\left(128\right)=1\times 2\times 8=16$$$$findthevalueof:$$$$\:\:\:\:\:{f}\:\left(\mathrm{100}\right)\:+\:{f}\left(\mathrm{101}\:\right)+\:{f}\:\left(\mathrm{102}\:\right)+…{f}\left(\mathrm{999}\right)=? \…