Question Number 143080 by Mathspace last updated on 09/Jun/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Answered by qaz last updated on 10/Jun/21 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 143081 by Mathspace last updated on 09/Jun/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} {xe}^{−{x}^{\mathrm{2}} } {arctanx}\:{dx} \\ $$ Answered by qaz last updated on 10/Jun/21 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 143082 by Mathspace last updated on 09/Jun/21 $${calculate}\:{f}\left({a},{b}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{ax}^{\mathrm{2}} } }{{x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} }{dx} \\ $$$${with}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$ Answered by Dwaipayan Shikari last…
Question Number 143083 by Mathspace last updated on 09/Jun/21 $${calculate}\:\Psi\left({a},{b}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{ax}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$$${with}\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$ Answered by Olaf_Thorendsen last…
Question Number 77536 by ~blr237~ last updated on 07/Jan/20 $$\mathrm{find}\:\mathrm{all}\:\mathrm{function}\:\mathrm{that}\:\mathrm{satisfy} \\ $$$$\:\:\forall\:\mathrm{p}>\mathrm{0}\:\:\:\int_{\mathrm{0}} ^{\infty} \mathrm{f}\left(\mathrm{t}\right)\mathrm{e}^{−\mathrm{pt}} \mathrm{dt}=\:\mathrm{e}^{−\mathrm{pT}} \:\:\:\:\:\:\mathrm{with}\:\mathrm{T}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{real} \\ $$ Answered by JDamian last updated on 07/Jan/20…
Question Number 143071 by cesarL last updated on 09/Jun/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{8}{dx}}{{tgx}+\mathrm{1}} \\ $$ Answered by TheSupreme last updated on 09/Jun/21 $${y}={tan}\left({x}\right) \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{y}^{\mathrm{2}} }{dy}={dx}…
Question Number 11998 by ajfour last updated on 09/Apr/17 Commented by ajfour last updated on 09/Apr/17 $${What}\:{distance}\:{does}\:{point}\:{P}\: \\ $$$${travel}\:{as}\:{the}\:{centre}\:{moves}\: \\ $$$${forward}\:{by}\:\mathrm{2}\pi{R}\:.\:{The}\:{disc} \\ $$$$\:{rolls}\:{witbout}\:{slipping}\:. \\ $$…
Question Number 11982 by tawa last updated on 08/Apr/17 $$\int\mathrm{x}^{\mathrm{5}} \left(\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}}\right)\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 08/Apr/17 $${I}=\frac{\mathrm{1}}{\mathrm{3}}\int{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{3}} +\mathrm{1}}\:\left(\mathrm{3}{x}^{\mathrm{2}} {dx}\right)…
Question Number 143051 by mnjuly1970 last updated on 09/Jun/21 $$\:\:\:\:\:\:\:_{\ast\ast\ast\ast\ast} ::\:\:{Lobachevsky}\:{Integral}\:::_{\ast\ast\ast\ast\ast} \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{s}{in}^{\mathrm{2}} \left(\:{tan}\left({x}\right)\right)}{{x}^{\:\mathrm{2}} }{dx}\overset{?} {=}\frac{\pi}{\mathrm{2}} \\ $$$$\:\:\:\:………. \\ $$ Answered by Olaf_Thorendsen…
Question Number 11937 by tawa last updated on 05/Apr/17 $$\int\frac{\mathrm{dx}}{\:\sqrt{\mathrm{5}\:+\:\mathrm{4x}\:−\:\mathrm{x}^{\mathrm{2}} }}\: \\ $$$$ \\ $$$$ \\ $$$$\mathrm{is}\:\mathrm{this}\:\mathrm{answer}\:\mathrm{correct}\:?\:\:\:\:\:\:\:\:\:\:\:−\mathrm{ln}\left[\mathrm{1}/\mathrm{4}\left(\mathrm{x}\:−\:\mathrm{5}\right)\:−\:\mathrm{ln6}\left(−\:\mathrm{1}\:−\:\mathrm{x}\right)\right]\:+\:\mathrm{C} \\ $$ Commented by ridwan balatif last updated…