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Category: Integration

cos-x-5-4cos-x-2-dx-

Question Number 87340 by john santu last updated on 04/Apr/20 $$\int\:\frac{\mathrm{cos}\:\mathrm{x}}{\left(\mathrm{5}+\mathrm{4cos}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}\:= \\ $$ Commented by john santu last updated on 04/Apr/20 $$\mathrm{dear}\:\mathrm{mr}\:\mathrm{Mjs}.\:\mathrm{whether}\:\mathrm{methods}\: \\ $$$$\mathrm{besides}\:\mathrm{weierstrass}\:\mathrm{substitution}?…

ln-x-x-2-1-1-2-1-ln-x-2-1-x-x-1-dx-

Question Number 152861 by talminator2856791 last updated on 02/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\: \\ $$$$\int_{−\infty} ^{\:\infty} \frac{\left(\mathrm{ln}\left(\left({x}^{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}} +\mathrm{1}\right)^{\mathrm{2}} +\mathrm{1}\right)\right)^{−\mathrm{ln}\left({x}^{\mathrm{2}} +\mathrm{1}\right)} }{\:\sqrt{{x}^{\mid\lfloor{x}\rfloor\mid} +\mathrm{1}}}\:\:{dx} \\ $$$$\: \\…

ln-x-4-1-ln-x-2-1-3-2-dx-

Question Number 152866 by talminator2856791 last updated on 02/Sep/21 $$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{ln}\left(\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}\right)}{\left(\mathrm{ln}\left(\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)^{\mathrm{3}} \right)\right)^{\mathrm{2}} }\:\:{dx} \\ $$$$\: \\ $$$$\: \\…

1-e-x-dx-2-sin-x-sin-x-cos-x-dx-

Question Number 87325 by M±th+et£s last updated on 04/Apr/20 $$\left.\mathrm{1}\right)\:\int{e}^{\sqrt{{x}}} \:{dx} \\ $$$$\left.\mathrm{2}\right)\int\frac{\sqrt{{sin}\left({x}\right)}}{\:\sqrt{{sin}\left({x}\right)}+\sqrt{{cos}\left({x}\right)}}{dx} \\ $$ Commented by Serlea last updated on 04/Apr/20 $$\left.\mathrm{1}\right)\:\int\mathrm{e}^{\sqrt{\mathrm{x}}} \mathrm{dx} \\…