Question Number 98445 by mathmax by abdo last updated on 14/Jun/20 $$\mathrm{give}\:\mathrm{at}\:\mathrm{form}\:\mathrm{of}\:\mathrm{serie}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{x}^{\mathrm{n}} \mathrm{ln}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by mathmax by abdo last…
Question Number 98428 by mathmax by abdo last updated on 13/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} \:\:,\mathrm{2}\pi\:\mathrm{periodi}\:\mathrm{even}\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated on 14/Jun/20 $$\mathrm{f}\:\mathrm{is}\:\mathrm{even}\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{a}_{\mathrm{0}}…
Question Number 98426 by mathmax by abdo last updated on 13/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{dt}}{\mathrm{x}+\mathrm{tant}}\:\:\mathrm{calculate}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{explicit}\:\mathrm{g}\left(\mathrm{x}\right)\:=\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{dt}}{\left(\mathrm{x}+\mathrm{tant}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{integrals}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{dt}}{\mathrm{2}+\mathrm{tant}}\:\mathrm{and}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{dt}}{\left(\mathrm{2}+\mathrm{tant}\right)^{\mathrm{2}}…
Question Number 98423 by mathmax by abdo last updated on 13/Jun/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }} \mathrm{dx} \\ $$ Answered by maths mind last updated…
Question Number 163954 by mnjuly1970 last updated on 12/Jan/22 Answered by mathmax by abdo last updated on 13/Jan/22 $$\Psi=\mathrm{2}\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{e}^{\mathrm{x}} }{\mathrm{sh}\left(\mathrm{2x}\right)}\mathrm{dx}\:=_{\mathrm{2x}=\mathrm{t}} \:\:\mathrm{2}\int_{\mathrm{0}} ^{\infty}…
Question Number 98382 by bobhans last updated on 13/Jun/20 $$\int\:\mathrm{tan}\:\mathrm{x}\:\sqrt{\mathrm{1}+\mathrm{tan}\:^{\mathrm{4}} \:\mathrm{x}}\:\mathrm{dx}\: \\ $$ Commented by john santu last updated on 13/Jun/20 $$\mathrm{set}\:\mathrm{tan}\:\mathrm{x}\:=\:\sqrt{\mathrm{z}}\:\Rightarrow\mathrm{x}\:=\:\mathrm{arc}\:\mathrm{tan}\:\left(\sqrt{\mathrm{z}}\right) \\ $$$$\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{z}}}\:×\frac{\mathrm{1}}{\mathrm{1}+\mathrm{z}^{\mathrm{2}} }\:\mathrm{dz}\:…
Question Number 98338 by M±th+et+s last updated on 13/Jun/20 $$\int{cos}\left({x}^{\mathrm{18}} \right)\:{dx} \\ $$$$ \\ $$ Answered by smridha last updated on 13/Jun/20 $$\boldsymbol{{let}}\:\boldsymbol{{x}}=\boldsymbol{{k}}^{\frac{\mathrm{1}}{\mathrm{18}}} \boldsymbol{{so}} \\…
Question Number 32789 by Ratnesh last updated on 02/Apr/18 $$\mid\underset{{a}} {\overset{{b}} {\int}}{f}\left({x}\right){dx}\leqslant\mid\underset{{a}} {\overset{{b}} {\int}}\mid{f}\left({x}\right)\mid{dx}\mid \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163854 by amin96 last updated on 11/Jan/22 $$\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{residu}}\:\boldsymbol{\mathrm{theorem}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{x}}^{\mathrm{4}} +\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{2}}\boldsymbol{\mathrm{dx}}=?\:\:\:\: \\ $$ Answered by Ar Brandon last updated…
Question Number 32785 by NECx last updated on 02/Apr/18 $$\int\frac{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}}{\mathrm{7}{x}^{\mathrm{2}} −\mathrm{9}{x}+\mathrm{2}}{dx} \\ $$ Answered by Joel578 last updated on 02/Apr/18 $$\frac{\mathrm{3}{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:−\:\mathrm{4}}{\left(\mathrm{7}{x}\:−\:\mathrm{2}\right)\left({x}\:−\mathrm{1}\right)}\:=\:\frac{{A}}{\mathrm{7}{x}\:−\:\mathrm{2}}\:+\:\frac{{B}}{{x}\:−\:\mathrm{1}}\:+\:{C} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{7}{Cx}^{\mathrm{2}}…