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Category: Integration

let-f-x-pi-4-pi-3-dt-x-tant-calculate-f-x-2-explicit-g-x-pi-4-pi-3-dt-x-tant-2-3-find-the-value-of-integrals-pi-4-pi-3-dt-2-tant-and-pi-4-pi-3-dt-2-tan

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-163954

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}…

tan-x-1-tan-4-x-dx-

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}\:…

cos-x-18-dx-

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}} \\…

solution-with-residu-theorem-0-x-2-x-4-2x-2-2-dx-

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…

3x-2-2x-4-7x-2-9x-2-dx-

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}}…