Question Number 32304 by abdo imad last updated on 22/Mar/18 $${find}\:{lim}_{{x}\rightarrow+\infty} \:\:{e}^{−{x}^{\mathrm{2}} } \:\int_{\mathrm{0}} ^{{x}} \:\:{e}^{{t}^{\mathrm{2}} } {dt}\:\:. \\ $$ Terms of Service Privacy Policy…
Question Number 32302 by abdo imad last updated on 22/Mar/18 $${calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\:\:\frac{{dx}}{{x}\:+{x}\sqrt{{x}}}\:. \\ $$ Answered by sma3l2996 last updated on 23/Mar/18 $${let}\:{t}=\sqrt{{x}}\Rightarrow{dx}=\mathrm{2}{tdt} \\ $$$${A}=\int_{\mathrm{1}}…
Question Number 97839 by mathmax by abdo last updated on 10/Jun/20 $$\mathrm{calculate}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\frac{\mathrm{n}\pi}{\mathrm{4}}} \:\frac{\mathrm{dx}}{\mathrm{3cos}^{\mathrm{4}} \mathrm{x}\:+\mathrm{3sin}^{\mathrm{4}} \mathrm{x}−\mathrm{1}} \\ $$ Commented by mr W last updated…
Question Number 32301 by abdo imad last updated on 22/Mar/18 $${calculate}\:\int_{\mathrm{1}} ^{{e}} \:{ln}\left(\mathrm{1}+\sqrt{{x}}\right){dx}\:. \\ $$ Commented by abdo imad last updated on 01/Apr/18 $${ch}.\:\sqrt{{x}}\:={t}\:{give}\:{I}\:=\:\int_{\mathrm{1}} ^{\sqrt{{e}}}…
Question Number 163357 by mnjuly1970 last updated on 06/Jan/22 $$ \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\mathrm{3}{x}−\mathrm{3}{x}^{\:\mathrm{2}} +\:{x}^{\:\mathrm{3}} \right)=\:? \\ $$$$ \\ $$ Answered by Ar Brandon last…
Question Number 163349 by smallEinstein last updated on 06/Jan/22 Answered by Ar Brandon last updated on 06/Jan/22 $${I}=\int_{−\infty} ^{\infty} \left(\int_{−\infty} ^{\infty} {e}^{−\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}\sqrt{\mathrm{2}}{xy}+\mathrm{3}{y}^{\mathrm{2}} \right)} {dx}\right){dy}…
Question Number 32269 by abdo imad last updated on 22/Mar/18 $${find}\:\int\:\:\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx} \\ $$ Answered by mrW2 last updated on 22/Mar/18 $$\int\:\:\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx}…
Question Number 97800 by abdomathmax last updated on 09/Jun/20 $$\left.\mathrm{1}\right)\:\mathrm{findf}\left(\mathrm{a}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{a}}\mathrm{dx}\:\:\:\:\:\mathrm{with}\:\mathrm{a}>\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\mathrm{explicite}\:\mathrm{g}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{a}}}\: \\ $$$$\left.\mathrm{3}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}\:+\mathrm{3}}} \\ $$…
Question Number 97794 by abdomathmax last updated on 09/Jun/20 $$\mathrm{solve}\:\mathrm{y}^{''} \:+\mathrm{y}\:=\frac{\mathrm{1}}{\mathrm{cosx}} \\ $$ Commented by john santu last updated on 10/Jun/20 $$\mathrm{y}''+\mathrm{y}'\:=\:\mathrm{sec}\:\mathrm{x} \\ $$$$\mathrm{homogenous}\:\mathrm{solution}\: \\…
Question Number 32258 by Cheyboy last updated on 22/Mar/18 $${find} \\ $$$$\int\:\frac{\mathrm{1}}{\mathrm{2}−{x}^{\mathrm{2}} }\:{dx} \\ $$ Answered by mrW2 last updated on 22/Mar/18 $$\int\:\frac{\mathrm{1}}{\left(\sqrt{\mathrm{2}}\right)^{\mathrm{2}} −{x}^{\mathrm{2}} }\:{dx}…