Question Number 87103 by hamdhan last updated on 02/Apr/20 $$\int\frac{{dx}}{\left(\mathrm{1}+{x}\right)\sqrt{{x}−{x}^{\mathrm{2}} }} \\ $$ Commented by abdomathmax last updated on 02/Apr/20 $${I}\:=\int\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{−\left({x}^{\mathrm{2}} −{x}\right)}}\:=\int\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{−\left({x}^{\mathrm{2}} −{x}\:+\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{4}}\right)}} \\ $$$$=\int\:\:\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{\frac{\mathrm{1}}{\mathrm{4}}−\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}}…
Question Number 87086 by Chi Mes Try last updated on 02/Apr/20 Answered by mind is power last updated on 03/Apr/20 $$=\int_{\mathrm{0}} ^{+\infty} \mathrm{2}\frac{{dt}}{\left({t}^{\mathrm{4}} +\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}}\right){t}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 87052 by lémùst last updated on 02/Apr/20 $${f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{sin}^{\mathrm{2}} \left({t}\right)}{\mathrm{1}+{xsin}^{\mathrm{2}} \left({t}\right)}{dt} \\ $$ Commented by mathmax by abdo last updated on 02/Apr/20…
Question Number 87048 by Ar Brandon last updated on 02/Apr/20 $${Express}\:\:{into}\:\:{partial}\:\:{fractions} \\ $$$$\:\:\:\:\:\:\:\:\frac{{x}^{\mathrm{6}} }{{x}^{\mathrm{12}} +\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 152580 by aupo14 last updated on 29/Aug/21 Answered by Lordose last updated on 29/Aug/21 $$\mathrm{I}\:=\:\int\mathrm{e}^{\mathrm{sec}^{\mathrm{2}} \left(\mathrm{x}\right)} \mathrm{tan}\left(\mathrm{x}\right)\mathrm{dx}\:\overset{\mathrm{u}=\mathrm{sec}\left(\mathrm{x}\right)} {=}\int\frac{\:\mathrm{e}^{\mathrm{u}^{\mathrm{2}} } }{\mathrm{u}}\mathrm{du}\:\overset{\mathrm{y}=\mathrm{u}^{\mathrm{2}} } {=}\:\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\:\mathrm{e}^{\mathrm{y}} }{\mathrm{y}}\mathrm{dy}…
Question Number 87046 by Tajaddin last updated on 02/Apr/20 $$\int\frac{{dx}}{{sin}^{\mathrm{3}} {x}+{cos}^{\mathrm{3}} {x}} \\ $$ Answered by MJS last updated on 02/Apr/20 $$\int\frac{{dx}}{\mathrm{sin}^{\mathrm{3}} \:{x}\:+\mathrm{cos}^{\mathrm{3}} \:{x}}= \\…
Question Number 152576 by Tawa11 last updated on 31/Aug/21 $$\int\:\frac{\mathrm{t}\:\:\:+\:\:\:\mathrm{13}}{\:\sqrt[{\mathrm{3}}]{\mathrm{t}^{\mathrm{2}} \:\:\:+\:\:\:\mathrm{5t}\:\:\:+\:\:\:\mathrm{6}}}\:\:\mathrm{dt} \\ $$ Commented by MATHkingElsenK last updated on 31/Aug/21 $${hello}\:\mathrm{5}{x}\:{no}\:\mathrm{5}{t} \\ $$ Terms of…
Question Number 152572 by rexford last updated on 29/Aug/21 $$\int_{−\frac{\Pi}{\mathrm{2}}} ^{\frac{\Pi}{\mathrm{2}}} \frac{\mathrm{1}+{cosx}}{\mathrm{3}+\mathrm{2}{sinx}}{dx} \\ $$$${please},{help}\:{me} \\ $$ Answered by Ar Brandon last updated on 29/Aug/21 $${I}=\int_{−\frac{\pi}{\mathrm{2}}}…
Question Number 87023 by john santu last updated on 02/Apr/20 $$\int\:\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{8x}+\mathrm{15}}}\:?\: \\ $$ Commented by john santu last updated on 02/Apr/20 $$\int\:\:\frac{{dx}}{\:\sqrt{\left({x}−\mathrm{4}\right)^{\mathrm{2}} −\mathrm{1}}}\:=\:{I} \\…
Question Number 87025 by john santu last updated on 02/Apr/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{arc}\:\mathrm{tan}\:\left(\sqrt{\mathrm{2}}\:\mathrm{tan}\:\mathrm{x}\right)}{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}?\: \\ $$ Commented by mathmax by abdo last updated on 02/Apr/20 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}}…