Question Number 119970 by bramlexs22 last updated on 28/Oct/20 $$\:\int\:\frac{{dx}}{{x}^{\mathrm{2}} \sqrt{\mathrm{25}−{x}^{\mathrm{2}} }}\:? \\ $$ Answered by bemath last updated on 28/Oct/20 $$\:\int\:\frac{{dx}}{{x}^{\mathrm{3}} \sqrt{\frac{\mathrm{25}}{{x}^{\mathrm{2}} }−\mathrm{1}}}\:{dx}\:=\:\int\:\frac{{x}^{−\mathrm{3}} }{\:\sqrt{\mathrm{25}{x}^{−\mathrm{2}}…
Question Number 119960 by mnjuly1970 last updated on 28/Oct/20 Answered by mathmax by abdo last updated on 28/Oct/20 $$\mathrm{A}\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctanx}}{\left(\mathrm{1}+\mathrm{x}\right)\sqrt{\mathrm{x}}}\mathrm{dx}\:\Rightarrow\mathrm{A}\:=_{\sqrt{\mathrm{x}}=\mathrm{t}} \:\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{t}^{\mathrm{2}} \right)}{\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}}…
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Question Number 185484 by Mingma last updated on 22/Jan/23 Answered by Ar Brandon last updated on 22/Jan/23 $${I}=\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} }{{e}^{\mathrm{3}{x}} −\mathrm{1}}{dx}=\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} {e}^{−\mathrm{3}{x}}…
Question Number 119934 by bramlexs22 last updated on 28/Oct/20 $$\:\:\:\int\:\frac{\mathrm{sin}\:^{\mathrm{8}} {x}−\mathrm{cos}\:^{\mathrm{8}} {x}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}}\:{dx}\: \\ $$ Answered by bobhans last updated on 28/Oct/20 $$\:\int\:\frac{\left(\mathrm{sin}\:^{\mathrm{4}} {x}−\mathrm{cos}\:^{\mathrm{4}} {x}\right)\left(\mathrm{sin}\:^{\mathrm{4}}…
Question Number 119930 by Lordose last updated on 28/Oct/20 Answered by mathmax by abdo last updated on 28/Oct/20 $$\mathrm{A}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{arcsin}\left(\mathrm{tan}\theta\right)\mathrm{d}\theta\:\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement} \\ $$$$\mathrm{arcsin}\left(\mathrm{tan}\theta\right)=\mathrm{x}\:\Rightarrow\mathrm{tan}\theta\:=\mathrm{sinx}\:\Rightarrow\theta\:=\mathrm{artan}\left(\mathrm{sinx}\right)\:\Rightarrow \\ $$$$\mathrm{A}\:=\int_{\mathrm{0}}…
Question Number 119920 by bramlexs22 last updated on 28/Oct/20 $$\:\int\:\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\:{dx}\:=\:?\:,\:{x}\epsilon\left(−\mathrm{1},\mathrm{1}\right) \\ $$ Answered by mathmax by abdo last updated on 28/Oct/20 $$\mathrm{I}\:=\int\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}}\mathrm{dx}\:\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{x}\:=\mathrm{cost}\:\Rightarrow \\ $$$$\mathrm{I}\:=\int\:\sqrt{\frac{\mathrm{2sin}^{\mathrm{2}} \left(\frac{\mathrm{t}}{\mathrm{2}}\right)}{\mathrm{2cos}^{\mathrm{2}}…
Question Number 185455 by cortano1 last updated on 22/Jan/23 $$\:\int\:\frac{{x}^{\mathrm{3}} .{e}^{{x}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:{dx}\:=? \\ $$ Answered by SEKRET last updated on 22/Jan/23 $$\left.\:\:\mathrm{1}\right)\:\:\:\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}}…
Question Number 185451 by mathlove last updated on 22/Jan/23 Commented by Frix last updated on 22/Jan/23 $$\mathrm{Yes}. \\ $$ Commented by mathlove last updated on…
Question Number 54376 by Abdo msup. last updated on 02/Feb/19 $$\left.\mathrm{1}\right)\:{calculate}\:\:{f}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:+{ax}\:\:+\mathrm{1}} \\ $$$${with}\:\:\:\mid{a}\mid<\mathrm{2} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{x}}{\left({x}^{\mathrm{2}} \:+{ax}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){find}\:{values}\:{of}\:{integrals}\:\int_{−\infty} ^{+\infty}…