Question Number 57749 by maxmathsup by imad last updated on 11/Apr/19 $${find}\:\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} \sqrt{\mathrm{9}+{x}^{\mathrm{2}} }} \\ $$ Commented by maxmathsup by imad last updated on 11/Apr/19…
Question Number 57750 by maxmathsup by imad last updated on 11/Apr/19 $${find}\:\int\:{x}^{\mathrm{2}} \sqrt{\mathrm{25}−{x}^{\mathrm{2}} }{dx}\: \\ $$ Answered by MJS last updated on 11/Apr/19 $$\int{x}^{\mathrm{2}} \sqrt{\mathrm{25}−{x}^{\mathrm{2}}…
Question Number 57748 by maxmathsup by imad last updated on 11/Apr/19 $${find}\:\int\:{x}^{\mathrm{2}} \sqrt{\mathrm{4}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last updated on 11/Apr/19…
Question Number 57746 by maxmathsup by imad last updated on 10/Apr/19 $${let}\:{f}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{xt}\:+\mathrm{1}\right)^{\mathrm{2}} }\:\:{with}\:\mid{x}\mid<\mathrm{1}\:\:\:\left({x}\:{real}\right) \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{tdt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{xt}\:+\mathrm{1}\right)^{\mathrm{3}} } \\…
Question Number 123261 by mnjuly1970 last updated on 24/Nov/20 $$\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\Omega=\int_{\mathbb{R}} {e}^{{x}−{sinh}^{\mathrm{2}} \left({x}\right)} {dx}=\sqrt{\pi} \\ $$ Answered by Olaf last…
Question Number 123255 by mnjuly1970 last updated on 24/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\ast\ast\ast\:\:{nice}\:\:{calculus}\:\ast\ast\ast \\ $$$$\:\:\:\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\Phi=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {log}^{\mathrm{3}} \left({tan}\left({x}\right)\right){dx}\:=? \\ $$ Answered by Dwaipayan Shikari last updated…
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Question Number 123234 by benjo_mathlover last updated on 24/Nov/20 $$\:\:\int\:\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}}\:{dx}\: \\ $$ Commented by liberty last updated on 24/Nov/20 Answered by MJS_new last updated…
Question Number 57667 by maxmathsup by imad last updated on 09/Apr/19 $${calculate}\:{U}_{{n}} =\int_{\frac{\pi}{{n}}} ^{\frac{\mathrm{2}\pi}{{n}}} \:\:\:\:\:\frac{{dx}}{\mathrm{2}\:+{sinx}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:\:\:\:\:\:\:{and}\:{lim}_{{n}\rightarrow+\infty} \:\:{nU}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Commented by…
Question Number 57668 by maxmathsup by imad last updated on 09/Apr/19 $${let}\:{V}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}+\frac{\mathrm{1}}{{n}}} \:\:\:\:\frac{{x}+\mathrm{1}}{\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{3}}}\:{dx}\:\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{V}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:{V}_{{n}} \\ $$ Commented by…