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 $$\left.\mathrm{1}\right)\:{calculate}\:{I}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} −{i}}\:\:\:{and}\:{J}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} −{i}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{1}} \\ $$…
Question Number 187703 by Tawa11 last updated on 20/Feb/23 $$\int\:\frac{\mathrm{1}}{\mathrm{5x}^{\mathrm{2}} \:\:−\:\:\mathrm{2x}\:\:−\:\:\mathrm{4}}\:\mathrm{dx} \\ $$ Answered by MikeH last updated on 20/Feb/23 $$=\:\frac{\mathrm{1}}{\mathrm{5}}\int\frac{\mathrm{1}}{{x}^{\mathrm{2}} −\frac{\mathrm{2}}{\mathrm{5}}{x}−\frac{\mathrm{4}}{\mathrm{5}}}\:{dx} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{5}}\int\frac{\mathrm{1}}{\left({x}−\frac{\mathrm{1}}{\mathrm{5}}\right)^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{25}}−\frac{\mathrm{4}}{\mathrm{5}}}{dx}…
Question Number 122160 by benjo_mathlover last updated on 14/Nov/20 Answered by liberty last updated on 14/Nov/20 $$\:\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\left[\:\mathrm{f}\left(\mathrm{x}\right)+\mathrm{1}\:\right]\:\mathrm{dx}\:−\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\left[\:\mathrm{f}\left(\mathrm{t}\right)+−\mathrm{1}\right]\:\mathrm{dt}\:= \\ $$$$\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}−\int_{\mathrm{0}}…
Question Number 122159 by mnjuly1970 last updated on 14/Nov/20 $$\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:\:{prove}\:\:{that}:: \\ $$$$\Omega=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left\{{tan}^{−\mathrm{1}} \left({ptan}\left({x}\right)\right)−{tan}^{−\mathrm{1}} \left({qtan}\left({x}\right)\right)\right\}\left({tan}\left({x}\right)+{cot}\left({x}\right)\right){dx} \\ $$$$=\frac{\pi}{\mathrm{2}}\:{log}\left(\frac{{p}}{{q}}\right)\:\:\:\left(\:\:\:\:{p}\:,\:{q}\:>\mathrm{0}\:\:\:\right) \\ $$$$\:\:\:\:{m}.{n}. \\ $$ Answered…