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 $$\int\:\frac{\mathrm{1}}{\left(\sqrt{\mathrm{2}}\right)^{\mathrm{2}} −{x}^{\mathrm{2}} }\:{dx}…
Question Number 97782 by 175 last updated on 09/Jun/20 $${Evaluate}: \\ $$$$\int\:\frac{{sinx}}{\mathrm{1}\:+{sin}^{\mathrm{2}} {x}}{dx} \\ $$ Commented by mr W last updated on 09/Jun/20 $$=−\int\frac{{d}\left(\mathrm{cos}\:{x}\right)}{\left(\sqrt{\mathrm{2}}−\mathrm{cos}\:{x}\right)\left(\sqrt{\mathrm{2}}+\mathrm{cos}\:{x}\right)} \\…
Question Number 97759 by bobhans last updated on 09/Jun/20 $$\int\:\frac{\mathrm{sin}\:^{\mathrm{5}} \left({x}\right)\:{dx}}{\:\sqrt{\mathrm{cos}\:\left({x}\right)}}\:? \\ $$ Answered by bemath last updated on 09/Jun/20 $$\int\:\frac{\left(\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}\right)^{\mathrm{2}} \mathrm{sin}\:{x}\:{dx}}{\:\sqrt{\mathrm{cos}\:{x}}}\:= \\ $$$${set}\:\sqrt{\mathrm{cos}\:{x}}\:=\:{z}\:\Rightarrow\:−\mathrm{sin}\:{x}\:{dx}\:=\:\mathrm{2}{z}\:{dz}…
Question Number 32206 by Glorious Man last updated on 21/Mar/18 $$\mathrm{Find}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\underset{\mathrm{k}−\mathrm{1}} {\overset{\mathrm{k}} {\int}}\mathrm{x}^{−\mathrm{x}} \:\mathrm{dx}\right)\:. \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 97721 by Power last updated on 09/Jun/20 Commented by mr W last updated on 09/Jun/20 Commented by smridha last updated on 09/Jun/20 $${this}\:{is}\:{not}\:\boldsymbol{{the}}\:\boldsymbol{{solution}}!!!…