Category: Integration

Question Number 127224 by mnjuly1970 last updated on 28/Dec/20 $$\dots calculus\left(I\right)-complexanalysis\dots$$$$calculate::$$$$\mathrm{\Phi }={\int }_0^{\mathrm{\infty }}\frac{ln\left(x\right)}{x^2+3x+2}dx=\frac{{ln}^2\left(2\right)}{2}$$$$$$ Answered by mindispower…

Question Number 61667 by aliesam last updated on 06/Jun/19 $$\int \sqrt{tan\left(x\right)}dx$$ Answered by MJS last updated on 06/Jun/19 $$\int \sqrt{\tan x}dx=$$$$[t=\sqrt{\tan x}\to dx={2\cos }^{2}x\sqrt{\tan x}dt]$$$$=\mathrm{2}\int\frac{{t}^{\mathrm{2}}…

Question Number 61661 by maxmathsup by imad last updated on 05/Jun/19 $$1)calculate\int {\int }_{R^{{+}^2}}\frac{dxdy}{(1+x^2)(1+y^2)}$$$$2)findthevalueof{\int }_0^{\mathrm{\infty }}\frac{ln\left(x\right)}{x^2-1}dx.$$ Commented…

Question Number 127190 by bramlexs22 last updated on 27/Dec/20 $$\int \frac{\sqrt{a}-\sqrt{x}}{1-\sqrt{ax}}dx=?;a>0$$ Answered by Dwaipayan Shikari last updated on 27/Dec/20 $$\Rightarrow ax=u^2\Rightarrow a=2u\frac{du}{dx}$$$$\mathrm{2}\int\frac{\sqrt{{a}}−\frac{{u}}{\:\sqrt{{a}}}}{\mathrm{1}−{u}}.\frac{{u}}{{a}}{du}\:=\:\frac{\mathrm{2}}{\:\sqrt{{a}^{\mathrm{3}} }}\int\frac{{a}−{u}}{\mathrm{1}−{u}}{du}=\frac{\mathrm{2}}{\:\sqrt{{a}^{\mathrm{3}}…

Question Number 61648 by maxmathsup by imad last updated on 05/Jun/19 $$calculate\int {\int }_W(x^2-2y^2)\sqrt{x^2+y^2+3}dxdywith$$$$W=\{(x,y)\in R^2/1⩽x⩽\sqrt{3}and{x}^2+y^2-2y⩽2\}$$ Commented…