Category: Integration

Question Number 3017 by Filup last updated on 03/Dec/15 $$A={\int }_{\mu }^{\mu +ϵ}\frac{dx}{x+n}$$$$$$$$A=\ln (x+n){\mid }_{\mu }^{\mu +ϵ}$$$$=\ln (\mu +ϵ+n)-\ln (\mu +n)$$$$=\ln \left(\frac{\mu +ϵ+n}{\mu +n}\right)$$$$=\ln (\frac{\mu +n}{\mu +n}+\frac{ϵ}{\mu +n})$$$$…

Question Number 134058 by john_santu last updated on 27/Feb/21 $$\mathcal{J}=\int \frac{dx}{1+\tan x+\csc x+\cot x+\sec x}$$ Answered by john_santu last updated on 27/Feb/21 $$\mathcal{J}=\int \frac{dx}{1+\frac{\sin x}{\cos x}+\frac{1}{\sin x}+\frac{\cos x}{\sin x}+\frac{1}{\cos x}}$$$$\:=\:\int\:\frac{\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}\mathrm{cos}\:{x}+\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{sin}\:{x}} \…

Question Number 134039 by Raxreedoroid last updated on 27/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 68481 by ajfour last updated on 11/Sep/19 $$I={\int }_0^1\sqrt{\frac{c-x^2}{x(1-x^2)}}dx(c>1)$$ Commented by MJS last updated on 11/Sep/19 $$\mathrm{I}\:\mathrm{tried}\:\mathrm{everything}\:\mathrm{I}\:\mathrm{know},\:\mathrm{it}\:\mathrm{seems}\:\mathrm{impossible} \…

Question Number 133973 by liberty last updated on 26/Feb/21 $$\mathrm{Given}\{\begin{array}{l}\mathrm{f}\left(\mathrm{x}\right)=\sqrt[3]{\mathrm{x}+\sqrt{{\mathrm{x}}^2+\frac{1}{27}}}+\sqrt[3]{\mathrm{x}-\sqrt{{\mathrm{x}}^2+\frac{1}{27}}}\\ \mathrm{g}\left(\mathrm{x}\right)={\mathrm{x}}^3+\mathrm{x}+1\end{array}$$$$\mathrm{Find}\underset{0}{\stackrel{4}{\int }}(\mathrm{g}\circ \mathrm{f}\circ \mathrm{g})\left(\mathrm{x}\right)\mathrm{dx}.$$ Answered by EDWIN88 last updated on…