Category: Integration

Question Number 43675 by maxmathsup by imad last updated on 13/Sep/18 $$calculate{\int }_1^2\frac{dx}{1+x^4}.$$ Commented by maxmathsup by imad last updated on…

Question Number 43657 by Tinkutara last updated on 13/Sep/18 Commented by maxmathsup by imad last updated on 24/Sep/18 $$letA=\int \frac{dx}{{(x^2+2x+10)}^2}wehaveA=\int \frac{dx}{{\{{(x+1)}^2+9\}}^2}$$$${changement}\:{x}+\mathrm{1}\:=\mathrm{3}{tan}\theta\:{give}\:…

Question Number 174696 by mnjuly1970 last updated on 08/Aug/22 $$$$$$\mathit{p}\mathit{r}\mathit{o}\mathit{v}\mathit{e}\mathit{t}\mathit{h}\mathit{a}\mathit{t}:$$$$$$$$\mathbf{\Omega }={\int }_0^{\mathrm{\infty }}{\left(\frac{\mathit{x}}{\mathit{s}\mathit{i}\mathit{n}\mathit{h}\left(\mathit{x}\right)}\right)}^3\mathit{d}\mathit{x}=\frac{{\mathit{\pi }}^2}{16}(12-{\mathit{\pi }}^2)$$$$\mathit{w}\mathit{r}\mathit{i}\mathit{t}\mathit{t}\mathit{e}\mathit{n}\mathit{a}\mathit{n}\mathit{d}\mathit{p}\mathit{r}\mathit{e}\mathit{p}\mathit{a}\mathit{r}\mathit{e}\mathit{d}\mathit{b}\mathit{y}:\mathit{m}.\mathit{n}$$$$…

Question Number 174685 by mnjuly1970 last updated on 08/Aug/22 $$$$$$provethat:$$$$$$$$\mathrm{\Omega }={\int }_0^{\mathrm{\infty }}\frac{x^2}{cosh\left(x\right)}dx=\frac{{\pi }^3}{8}$$$$$$ Answered…

Question Number 109129 by bemath last updated on 21/Aug/20 $$\underset{0}{\stackrel{\pi /2}{\int }}\frac{\ln \left(\cos x\right)\ln \left(\sin x\right)}{\tan x}dx$$ Answered by EmericGent last updated on 21/Aug/20 $$=\:{I}\:=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{ln}\left(\mathrm{1}-{sin}^{\mathrm{2}} {x}\right){ln}\left({sin}\:{x}\right)}{{sin}\:{x}}\:{cos}\:{x}\:{dx}…