Category: Integration

Question Number 79352 by M±th+et£s last updated on 24/Jan/20 $$\int \frac{dx}{1-\sqrt{cos\left(x\right)}}$$ Commented by mr W last updated on 24/Jan/20 $$nosolutionwithelementaryfunctions.$$$$ordoyouknowasolution?$$…

Question Number 79325 by Henri Boucatchou last updated on 24/Jan/20 $$\mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{g}\mathit{e}\mathit{n}\mathit{c}\mathit{e}\mathit{o}\mathit{f}:$$$$1)\mathit{I}={\int }_1^{\mathrm{\infty }}\frac{{\mathit{e}}^{-\mathit{t}/5}\mid \mathit{s}\mathit{i}\mathit{n}\left(\mathit{l}\mathit{n}\mathit{t}\right)\mid }{{(\mathit{t}-1)}^{3/2}}\mathit{d}\mathit{t}$$$$2)\mathit{I}={\int }_1^{\mathrm{\infty }}\frac{\sqrt{\mathit{l}\mathit{n}\mathit{x}}}{(\mathit{x}-1)\sqrt{\mathit{x}}}\mathit{d}\mathit{x}$$ Commented by…

Question Number 144815 by mnjuly1970 last updated on 29/Jun/21 Answered by mindispower last updated on 30/Jun/21 $$={\int }_0^{\mathrm{\infty }}\frac{sin(x+\sqrt{1+x^2})+sin(\sqrt{1+x^2}-x)}{2\sqrt{1+x^2}}dx$$$${x}={sh}\left({t}\right) \…

Question Number 144792 by imjagoll last updated on 29/Jun/21 $$\int \frac{{2\mathrm{x}}^3-1}{{\mathrm{x}}^4+\mathrm{x}}\mathrm{dx}?$$ Answered by liberty last updated on 29/Jun/21 $$\:\Omega=\int\:\frac{\mathrm{2x}^{\mathrm{3}} −\mathrm{1}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}}\:\mathrm{dx}\:=\:\int\:\frac{\mathrm{2x}−\mathrm{x}^{−\mathrm{2}} }{\mathrm{x}^{\mathrm{2}}…

Question Number 144788 by nonh1 last updated on 29/Jun/21 Answered by gsk2684 last updated on 30/Jun/21 $$\underset{\mathrm{x}=0}{\stackrel{1}{\int }}\left(\underset{\mathrm{y}=-3}{\stackrel{3}{\int }}(4-{\mathrm{y}}^2)\mathrm{dy}\right)\mathrm{dx}$$$$\underset{\mathrm{0}} {\overset{\mathrm{1}}…