Category: Integration

Question Number 150647 by puissant last updated on 14/Aug/21 Answered by puissant last updated on 14/Aug/21 $$posons{I}_{2n}={\int }_0^{\frac{\pi }{2}}{\left(sint\right)}^{2n}dt$$$$=\frac{1\times 3\times 5\dots \dots \times (2n-1)}{2\times 4\times 6\times \dots ..\times 2n}\times \frac{\pi }{2}$$$$\Rightarrow\:\:{I}_{\mathrm{2}{n}}…

Question Number 150627 by puissant last updated on 14/Aug/21 $${\int }_0^1\frac{{(-1)}^{E\left(\frac{1}{x}\right)}dx}{x}$$ Answered by puissant last updated on 14/Aug/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(−\mathrm{1}\right)^{{E}\left(\frac{\mathrm{1}}{{x}}\right)}…

Question Number 85009 by mathmax by abdo last updated on 18/Mar/20 $$calculate{\int }_0^{\mathrm{\infty }}\frac{x^n}{sh\left(x\right)}dxwithnintegrnatural$$ Commented by mathmax by abdo last updated on…

Question Number 19457 by NEC last updated on 11/Aug/17 $$provethat\int \tan {}^{2}xdx$$$$$$$$=\tan x-x$$ Answered by Joel577 last updated on 11/Aug/17 $$\int\:\mathrm{tan}^{\mathrm{2}}…

Question Number 84957 by john santu last updated on 17/Mar/20 $$\int {(2-{\mathrm{x}}^2)}^3\mathrm{dx}=$$ Commented by john santu last updated on 17/Mar/20 $$\int\:\left(\mathrm{8}−\mathrm{3}\left(\mathrm{4x}^{\mathrm{2}} \right)+\mathrm{3}\left(\mathrm{2x}^{\mathrm{4}}…