Question Number 147061 by liberty last updated on 17/Jul/21 $$\:\:\:\:\:\int_{\:\mathrm{0}\:} ^{\:\infty} \:\frac{{x}^{{a}} }{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)}\:\frac{{dx}}{{x}}\:=?\: \\ $$$$\:\:\mathrm{0}<{a}<\mathrm{3}\:\: \\ $$ Answered by Ar Brandon last updated on…
Question Number 147060 by ArielVyny last updated on 17/Jul/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {e}^{\mathrm{2}{x}} \sqrt{{tanx}}{dx} \\ $$ Answered by mathmax by abdo last updated on 17/Jul/21 $$\Psi=\int_{\mathrm{0}}…
Question Number 147035 by rs4089 last updated on 17/Jul/21 $${using}\:{residue}\:{theorem} \\ $$$${evaluate}\:\:\int_{\mid{z}\mid=\mathrm{3}} \frac{{zsecz}}{\left({z}−\mathrm{1}\right)^{\mathrm{2}} }{dz} \\ $$ Answered by mathmax by abdo last updated on 17/Jul/21…
Question Number 81482 by Bash last updated on 13/Feb/20 $${Evaluate}\:\:\int_{−\infty} ^{\infty} \frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{13}}. \\ $$ Commented by abdomathmax last updated on 13/Feb/20 $${I}=\int_{−\infty} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{2}}…
Question Number 146996 by ArielVyny last updated on 17/Jul/21 $$\int{ln}\left({cht}\right){dt} \\ $$ Answered by mathmax by abdo last updated on 17/Jul/21 $$\int\:\mathrm{log}\left(\mathrm{cht}\right)\mathrm{dt}\:=\int\:\mathrm{log}\left(\frac{\mathrm{e}^{\mathrm{t}} \:+\mathrm{e}^{−\mathrm{t}} }{\mathrm{2}}\right)\mathrm{dt} \\…
Question Number 81433 by abdomathmax last updated on 13/Feb/20 $${calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\:\:\:\:\frac{\mathrm{2}{x}+\mathrm{3}}{\left({x}−\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Answered by MJS last updated on 13/Feb/20 $$\int\frac{\mathrm{2}{x}+\mathrm{3}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 81432 by abdomathmax last updated on 13/Feb/20 $${find}\:\:\int\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} } \\ $$ Commented by abdomathmax last updated on 20/Feb/20 $${let}\:{try}\:{complex}\:{method}\:{I}\:=\int\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}}…
Question Number 81427 by abdomathmax last updated on 13/Feb/20 $$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{3}} \right){dx} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{{n}} \right){dx}\:{with}\:{n}\geqslant\mathrm{2} \\ $$ Commented by mind is power…
Question Number 146962 by Sameza last updated on 16/Jul/21 Answered by Olaf_Thorendsen last updated on 16/Jul/21 $$ \\ $$$$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{4}} \frac{\sqrt{{x}}}{\:\sqrt{\mathrm{4}−{x}}−\sqrt{{x}}}\:{dx}\:\:\:\left(\mathrm{1}\right) \\ $$$$\mathrm{Let}\:{u}\:=\:\mathrm{4}−{x} \\ $$$$\mathrm{I}\:=\:\int_{\mathrm{0}}…
Question Number 81400 by mind is power last updated on 12/Feb/20 $${Hello}\:\:{Nice}\:{day}\:{im}\:{thinking}\:{of}\:{this}\:{one}\:\:{a}\:{close}\:{forme}? \\ $$$$\int\sqrt{\mathrm{1}+{x}^{{p}} }{dx} \\ $$$${p}\in\mathbb{R}_{+} , \\ $$$${x}\in\left[\mathrm{0},\mathrm{1}\left[\right.\right. \\ $$ Commented by abdomathmax…