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Category: Integration

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

Question Number 12463 by tawa last updated on 23/Apr/17 $$\int\:\:\frac{\mathrm{x}\:+\:\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2x}\:+\:\mathrm{3}\right)^{\mathrm{2}/\mathrm{3}} }\:\:\mathrm{dx} \\ $$ Answered by ridwan balatif last updated on 23/Apr/17 $$\int\frac{\mathrm{x}+\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{3}\right)^{\mathrm{2}} }}\mathrm{dx}…

sin-3-7x-dx-

Question Number 12464 by tawa last updated on 23/Apr/17 $$\int\:\mathrm{sin}^{\mathrm{3}} \left(\mathrm{7x}\right)\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 23/Apr/17 $$\mathrm{sin}\:\mathrm{3}{x}=\mathrm{3sin}\:{x}−\mathrm{4sin}\:^{\mathrm{3}} {x} \\ $$$${I}=\int\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{7}{x}\right){dx}…

Calculus-i-1-0-1-ln-2-1-x-ln-x-x-dx-ii-2-0-1-ln-2-x-ln-1-x-x-dx-iii-3-0-1-ln-2-x-ln-1-x-x-dx-

Question Number 143508 by mnjuly1970 last updated on 15/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:……….{Calculus}…….. \\ $$$$\:\:\:\:{i}:\:\:\:\boldsymbol{\phi}_{\mathrm{1}} :=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right).{ln}\left({x}\right)}{{x}}{dx} \\ $$$$\:\:\:{ii}:\:\:\:\boldsymbol{\phi}_{\mathrm{2}} :=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left({x}\right).{ln}\left(\mathrm{1}−{x}\right)}{{x}}\:{dx} \\…

dx-x-x-dx-

Question Number 12436 by tawa last updated on 22/Apr/17 $$\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{x}} }\:\mathrm{dx} \\ $$ Commented by mrW1 last updated on 22/Apr/17 $${do}\:{you}\:{mean}\:\int\frac{{dx}}{{x}^{{x}} }\:? \\ $$$${I}\:{don}'{t}\:{think}\:{x}^{{x}} \:{as}\:{well}\:{as}\:{x}^{−{x}}…