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Category: Integration

3sinx-4cosx-4sinx-3cosx-dx-

Question Number 69502 by 20190927 last updated on 24/Sep/19 $$\int\frac{\mathrm{3sinx}+\mathrm{4cosx}}{\mathrm{4sinx}+\mathrm{3cosx}}\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 24/Sep/19 $${let}\:{I}\:=\int\:\:\frac{\mathrm{3}{sinx}\:+\mathrm{4}{cosx}}{\mathrm{4}{sinx}\:+\mathrm{3}{cosx}}{dx}\:\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\ $$$${I}\:=\int\frac{\mathrm{3}\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }+\mathrm{4}\frac{\mathrm{1}−{t}^{\mathrm{2}}…

Question-134962

Question Number 134962 by 0731619177 last updated on 09/Mar/21 Answered by Olaf last updated on 09/Mar/21 $$\forall{x}\in\mathbb{R}^{\ast} ,\:\mathrm{arctan}{x}+\mathrm{arctan}\frac{\mathrm{1}}{{x}}\:=\:\frac{\pi}{\mathrm{2}} \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\infty} \frac{{x}\mathrm{arctan}{x}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\…

0-2-1-x-3-x-2-2x-1-3-dx-

Question Number 134947 by bobhans last updated on 08/Mar/21 $$\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\left(\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} \:}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}}\:\right)\mathrm{dx}\:?\: \\ $$ Answered by EDWIN88 last updated on 09/Mar/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\:\mathrm{2}}…

let-f-0-cos-1-x-2-1-x-2-dx-1-determine-a-explicit-form-of-f-2-calculate-0-cos-2-2x-2-x-2-1-dx-

Question Number 69375 by mathmax by abdo last updated on 22/Sep/19 $${let}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\alpha\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\mathrm{2}+\mathrm{2}{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\…