Category: Integration

Question Number 61719 by aliesam last updated on 06/Jun/19 $$\int \frac{dx}{2+sin\left(x\right)}$$ Commented by maxmathsup by imad last updated on 07/Jun/19 $${let}\:{A}\:=\:\int\:\:\frac{{dx}}{\mathrm{2}+{sinx}}\:\Rightarrow{A}\:=_{{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}} \:\:\:\int\:\:\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }}\:\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}} }…

Question Number 127237 by bramlexs22 last updated on 28/Dec/20 $$Nice\dots \int \frac{\sqrt{1-\ln {}^2\left(x\right)}}{x\ln \left(x\right)}dx$$$$\int \sqrt{\frac{x}{1-x^3}}dx$$$$\int \sqrt{\frac{4-x}{x}}dx$$ Commented by bramlexs22 last updated on 28/Dec/20…

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…