Category: Integration

Question Number 142116 by Eric002 last updated on 26/May/21 $$usetrigonometricsubstitutiontosolve$$$$\int \frac{x^3}{\sqrt{9-x^2}}dx$$ Answered by ZiYangLee last updated on 27/May/21 $$\int\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{9}−{x}^{\mathrm{2}}…

Question Number 76572 by john santu last updated on 28/Dec/19 $$howdoyoufindtheleastvalueof{x}^2$$$$+2xy+3y^2-6x-2yusingthe$$$$conceptsofalgebraorcalculus?$$ Answered by benjo 1/2 santuyy last updated…

Question Number 142060 by iloveisrael last updated on 26/May/21 Answered by Ar Brandon last updated on 26/May/21 $$\mathrm{I}=\int \frac{1}{{\mathrm{x}}^2}{\mathrm{e}}^{\frac{1}{\mathrm{x}}}\sec (1+{\mathrm{e}}^{\frac{1}{\mathrm{x}}})\tan (1+{\mathrm{e}}^{\frac{1}{\mathrm{x}}})\mathrm{dx}$$$${u}=\mathrm{1}+\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \Rightarrow\mathrm{d}{u}=−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}}…

Question Number 76468 by kaivan.ahmadi last updated on 27/Dec/19 $$\int \frac{1-x^2-8x+1}{x^4-x^3-x+1}dx$$ Commented by mr W last updated on 27/Dec/19 $${why}\:{did}\:{you}\:{write}\:\mathrm{1}−{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{1}…

Question Number 76469 by kaivan.ahmadi last updated on 27/Dec/19 $$\int cothxdx$$ Commented by mathmax by abdo last updated on 27/Dec/19 $$\int\:{coth}\left({x}\right){dx}\:=\int\:\frac{{ch}\left({x}\right)}{{sh}\left({x}\right)}{dx}\:=\int\:\:\frac{{e}^{{x}} \:+{e}^{−{x}} }{{e}^{{x}} −{e}^{−{x}}…