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Question Number 214857 by MrGaster last updated on 21/Dec/24 $${\int }_0^1\ln \left(x\right)\ln (1+x)\ln (1-x)dx=?$$ Answered by MathematicalUser2357 last updated on 22/Dec/24 $$\mathbf{Wait}\dots \mathrm{They}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{integrate}\mathrm{it}\mathrm{like}\mathrm{I}\mathrm{integrate}\mathrm{it}\dots$$$$\mathrm{0}.\mathrm{139326}… \…

Question Number 214853 by liuxinnan last updated on 21/Dec/24 $$\int \frac{1+\cos x}{1+\sin {}^{2}x}dx=?$$ Commented by liuxinnan last updated on 21/Dec/24 $$Ihadlongtimenotlookthrough$$$$thisapp,Ijustfind$$…

Question Number 214729 by MathematicalUser2357 last updated on 18/Dec/24 $$\mathrm{Emergency}$$$$\frac{x(x+1)}{2}=\frac{2x-3}{3}+1$$ Answered by MATHEMATICSAM last updated on 18/Dec/24 $$\frac{x(x+1)}{2}=\frac{2x-3}{3}+1$$$$\Rightarrow\:\frac{{x}^{\mathrm{2}} \:+\:{x}}{\mathrm{2}}\:=\:\frac{\mathrm{2}{x}}{\mathrm{3}}…

Question Number 214683 by MATHEMATICSAM last updated on 16/Dec/24 Commented by MATHEMATICSAM last updated on 16/Dec/24 $$\mathrm{Circles}\mathrm{C}1\mathrm{and}\mathrm{C}2\mathrm{have}\mathrm{equal}\mathrm{radii}\mathrm{and}$$$$\mathrm{are}\mathrm{tangent}\mathrm{to}\mathrm{the}\mathrm{same}\mathrm{line}\mathrm{XY}.\mathrm{Circle}$$$$\mathrm{C}3\mathrm{is}\mathrm{tangent}\mathrm{to}\mathrm{C}1\mathrm{and}\mathrm{C}2.\mathrm{Find}$$$$\mathrm{distance}h,\mathrm{from}\mathrm{the}\mathrm{centre}\mathrm{of}\mathrm{C}3\mathrm{to}\mathrm{line}$$$$\mathrm{XY}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{x}\:\mathrm{and}\:\mathrm{radii}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circles}.…

Question Number 214667 by issac last updated on 16/Dec/24 $${\mathrm{let}}^{\prime }\mathrm{s}\mathrm{define}\mathrm{linear}\mathrm{differantial}\mathrm{operator}\mathcal{D}$$$$\mathrm{as}\mathcal{D}=z\cdot \frac{\mathrm{d}}{\mathrm{d}z}(z\cdot \frac{\mathrm{d}}{\mathrm{d}z})+z(1-{\left(\frac{\alpha }{z}\right)}^2)$$$$\mathrm{when}$$$$\mathcal{D}f\left(z\right)=\{z\cdot \frac{\mathrm{d}}{\mathrm{d}z}(z\cdot \frac{\mathrm{d}}{\mathrm{d}z})+z(1-{\left(\frac{\alpha }{z}\right)}^2)\}f\left(z\right)=0$$$$f\left(z\right)=?$$ Terms of Service…