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Category: Integration

2-2x-1-1-3-x-3-1-

Question Number 124452 by liberty last updated on 03/Dec/20 $$\:\mathrm{2}\:\sqrt[{\mathrm{3}}]{\mathrm{2}{x}+\mathrm{1}}\:=\:{x}^{\mathrm{3}} −\mathrm{1}\: \\ $$ Commented by Dwaipayan Shikari last updated on 03/Dec/20 $${Golden}\:{ratio}\:\phi=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}=\mathrm{1}.\mathrm{6180}.. \\ $$ Answered…

Prove-that-e-x-x-4-2-1-x-2-5-2-dx-e-x-1-x-2-x-1-x-2-3-2-C-

Question Number 124421 by Ar Brandon last updated on 03/Dec/20 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\int\mathrm{e}^{\mathrm{x}} \centerdot\frac{\mathrm{x}^{\mathrm{4}} +\mathrm{2}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}} }\mathrm{dx}=\frac{\mathrm{e}^{\mathrm{x}} \left\{\mathrm{1}+\mathrm{x}^{\mathrm{2}} +\mathrm{x}\right\}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} }+\mathrm{C} \\ $$ Commented by…

Question-189949

Question Number 189949 by Universmathematiques last updated on 24/Mar/23 Answered by witcher3 last updated on 25/Mar/23 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}\sqrt[{\mathrm{2}}]{\mathrm{x}\sqrt[{\mathrm{3}}]{\mathrm{x}\sqrt[{\mathrm{4}}]{}}…} \\ $$$$\mathrm{ln}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{ln}\left(\mathrm{x}\right)+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\left(\mathrm{x}\right)+\frac{\mathrm{1}}{\mathrm{6}}\mathrm{ln}\left(\mathrm{x}\right)….. \\ $$$$\mathrm{ln}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{k}!}=\mathrm{ln}\left(\underset{\mathrm{k}\geqslant\mathrm{1}} {\prod}\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{k}!}} \right)=\mathrm{ln}\left(\mathrm{x}^{\underset{\mathrm{m}\geqslant\mathrm{1}}…

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

Question Number 124371 by bemath last updated on 02/Dec/20 $$\:\int\:\frac{{e}^{{x}} \left(\mathrm{2}−\mathrm{sin}\:\mathrm{2}{x}\right)}{\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}}\:{dx}\: \\ $$ Commented by Dwaipayan Shikari last updated on 02/Dec/20 $$\int{e}^{{x}} \left(\frac{\mathrm{1}}{{sin}^{\mathrm{2}} {x}}−\frac{{cosx}}{{sinx}}\right){dx} \\…

0-4pi-cosx-

Question Number 124352 by Mammadli last updated on 02/Dec/20 $$\underset{\mathrm{0}} {\overset{\mathrm{4}\pi} {\int}}\parallel{cosx}\parallel=? \\ $$ Commented by mr W last updated on 02/Dec/20 $${do}\:{you}\:{mean}\:\underset{\mathrm{0}} {\overset{\mathrm{4}\pi} {\int}}\mid{cosx}\mid\:{dx}\:?…