Question Number 143261 by Mathspace last updated on 12/Jun/21 $${find}\:{Y}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)….\left({x}+{n}\right)} \\ $$$$\left({n}>\mathrm{1}\:{integr}\right) \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $$…
Question Number 143262 by Mathspace last updated on 12/Jun/21 $${developp}\:{at}\:{fourier}\:{serie} \\ $$$${f}\left({x}\right)=\frac{\mathrm{1}}{{cosx}\:+\mathrm{2}{sinx}} \\ $$ Answered by mathmax by abdo last updated on 13/Jun/21 $$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{cosx}+\mathrm{2sinx}}\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\frac{\mathrm{e}^{\mathrm{ix}} +\mathrm{e}^{−\mathrm{ix}}…
Question Number 143256 by Mathspace last updated on 12/Jun/21 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \int_{{x}} ^{\mathrm{2}−{x}} {e}^{−{xy}} \sqrt{{x}+{y}}{dy}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143257 by Mathspace last updated on 12/Jun/21 $${find}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]} {e}^{−\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)} {arctan}\left(\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right){dxdy} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143259 by Mathspace last updated on 12/Jun/21 $${solve}\:{y}^{''} −{y}^{'} +\mathrm{2}={xsin}\left(\mathrm{3}{x}\right) \\ $$ Answered by qaz last updated on 12/Jun/21 $$\mathrm{y}_{\mathrm{p}} =\frac{\mathrm{1}}{\mathrm{D}^{\mathrm{2}} −\mathrm{D}}\left[\mathrm{xsin}\:\left(\mathrm{3x}\right)−\mathrm{2}\right] \\…
Question Number 143258 by Mathspace last updated on 12/Jun/21 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \int_{{x}} ^{{x}^{\mathrm{2}} } \:\frac{{sh}\left({xt}\right)}{{x}+{t}}{dt} \\ $$ Answered by Mathspace last updated on 13/Jun/21 $$\int_{{x}} ^{{x}^{\mathrm{2}}…
Question Number 143255 by Mathspace last updated on 12/Jun/21 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{sin}\left(\mathrm{1}−{cosx}\right)+\mathrm{1}−{cos}\left({sinx}\right)}{{x}^{\mathrm{2}} } \\ $$ Answered by bramlexs22 last updated on 12/Jun/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{sin}\:\left(\mathrm{1}−\mathrm{cos}\:{x}\right)}{\mathrm{1}−\mathrm{cos}\:{x}}.\left(\mathrm{1}−\mathrm{cos}\:{x}\right)+\mathrm{1}−\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)}{{x}^{\mathrm{2}} } \\…
Question Number 143253 by Mathspace last updated on 12/Jun/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({x}^{\mathrm{3}} \right)}{\mathrm{1}+{x}^{\mathrm{3}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143254 by Mathspace last updated on 12/Jun/21 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)} \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $${R}\left({n}\right)\:=\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}…
Question Number 12137 by Gaurav3651 last updated on 14/Apr/17 Terms of Service Privacy Policy Contact: info@tinkutara.com