Question Number 122290 by mnjuly1970 last updated on 15/Nov/20 $$\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$\:\:\:{calculate}\::: \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}^{\mathrm{2}} \left(\psi\left(\mathrm{1}+{x}\right)−\psi\left(\mathrm{2}−{x}\right)\right){dx}=??? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}.\mathrm{1970}. \\ $$ Commented by Dwaipayan Shikari…
Question Number 56747 by Tawa1 last updated on 22/Mar/19 $$\int\:\mathrm{x}^{\mathrm{2}\:} \mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \:\:\mathrm{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 22/Mar/19 $$\int{x}^{\mathrm{2}} \left(\mathrm{1}+{x}^{\mathrm{2}} +\frac{{x}^{\mathrm{4}}…
Question Number 122274 by benjo_mathlover last updated on 15/Nov/20 $$\:\:\:\int\:\frac{\sqrt{\mathrm{1}−\sqrt{{x}}}}{\:\sqrt{\mathrm{1}+\sqrt{{x}}}}\:{dx}\:?\: \\ $$ Answered by liberty last updated on 15/Nov/20 $$\mathrm{let}\:\sqrt{\mathrm{x}}\:=\:\mathrm{cos}\:\theta\:\Rightarrow\:\mathrm{x}=\mathrm{cos}\:^{\mathrm{2}} \theta\: \\ $$$$\Rightarrow\:\mathrm{dx}\:=−\mathrm{2sin}\:\theta\:\mathrm{cos}\:\theta\:\mathrm{d}\theta\: \\ $$$$\mathrm{I}\:=\int\:\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:\theta}}{\:\sqrt{\mathrm{1}+\mathrm{cos}\:\theta}}\:\left(−\mathrm{2sin}\:\theta\:\mathrm{cos}\:\theta\:\right)\mathrm{d}\theta…
Question Number 56700 by maxmathsup by imad last updated on 21/Mar/19 $$\:{find}\:\int\:\sqrt{{x}−\mathrm{2}\sqrt{{x}}+\mathrm{3}}{dx} \\ $$ Commented by kaivan.ahmadi last updated on 22/Mar/19 Commented by maxmathsup by…
Question Number 56699 by maxmathsup by imad last updated on 21/Mar/19 $${let}\:{f}_{{n}} \left({a}\right)=\int_{−\infty} ^{\infty} \:\:\frac{{sin}\left({x}^{{n}} \right)}{{x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} }\:{dx}\:\:\:{with}\:{a}\:{positif}\:{real}\:{not}\:\mathrm{0}\:\:{and}\:{n}\:{from}\:{N} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:{g}_{{n}} \left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{sin}\left({x}^{{n}}…
Question Number 56698 by maxmathsup by imad last updated on 21/Mar/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{4}} \:+\mathrm{4}}{dx} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 122205 by mathmax by abdo last updated on 14/Nov/20 $$\mathrm{find}\:\int\:\:\frac{\mathrm{dx}}{\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}}} \\ $$ Commented by liberty last updated on 15/Nov/20 $$\:\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:=\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}}…
Question Number 122186 by physicstutes last updated on 14/Nov/20 $$\mathrm{Obtain}\:\mathrm{a}\:\mathrm{reduction}\:\mathrm{formulae}\:\mathrm{for}\: \\ $$$$\:\:\:{I}_{{n}} \:=\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\left(\mathrm{ln}\:{x}\right)^{{n}} {dx}\: \\ $$$$\mathrm{find}\:{I}_{\mathrm{2}} =\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} \:{dx} \\ $$ Answered…
Question Number 187700 by cortano12 last updated on 20/Feb/23 $$\:{Find}\:{minimum}\:{area}\:{of}\:{the}\:{part} \\ $$$$\:{y}={x}^{\mathrm{2}} \:{and}\:{y}={kx}\left({x}^{\mathrm{2}} −{k}\right),\:{k}>\mathrm{0}\: \\ $$ Commented by cortano12 last updated on 21/Feb/23 Terms of…
Question Number 56629 by maxmathsup by imad last updated on 19/Mar/19 $$\left.\mathrm{1}\right)\:{calculate}\:{I}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} −{i}}\:\:\:{and}\:{J}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} −{i}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{1}} \\ $$…