Category: Integration

Question Number 78797 by TawaTawa last updated on 20/Jan/20 $$\mathrm{Show}\mathrm{that}:{\int }_0^{\mathrm{\infty }}\frac{{\mathrm{x}}^3}{{\mathrm{e}}^{\mathrm{x}}-1}\mathrm{dx}=\frac{{\pi }^4}{15}$$ Answered by mind is power last updated on…

Question Number 144322 by qaz last updated on 24/Jun/21 $$\underset{\mathrm{n}=0}{\sum ^{\mathrm{\infty }}}\frac{\left(2\mathrm{n}\right)!!}{(2\mathrm{n}+1)!!(\mathrm{n}+1)}{\mathrm{x}}^{2\mathrm{n}+2}=?\dots \dots \dots .\mid \mathrm{x}\mid ⩽1$$ Answered by mindispower last updated on 25/Jun/21 $$\left(\mathrm{2}{n}\right)!!=\mathrm{2}^{{n}} .{n}! \…

Question Number 144248 by Pagnol last updated on 23/Jun/21 Answered by Ar Brandon last updated on 23/Jun/21 $$\mathrm{I}=\int {\tan }^7\mathrm{xdx}=\int {\tan }^5\mathrm{x}({\sec }^2\mathrm{x}-1)\mathrm{dx}$$$$\:\:=\frac{\mathrm{tan}^{\mathrm{6}} \mathrm{x}}{\mathrm{6}}−\int\mathrm{tan}^{\mathrm{3}} \mathrm{x}\left(\mathrm{sec}^{\mathrm{2}}…

Question Number 144245 by ArielVyny last updated on 23/Jun/21 $${\int }_0^1\frac{x^{2n}}{{(x-1)}^n}dx$$ Answered by mathmax by abdo last updated on 23/Jun/21…

Question Number 78706 by abdomathmax last updated on 20/Jan/20 $$calculate\int {\int }_{{[0,1]}^2}\frac{dxdy}{{(x+y+1)}^2}$$ Answered by mind is power last updated on 20/Jan/20 $$=\int_{\mathrm{0}}…