Category: Integration

Question Number 219620 by Nicholas666 last updated on 29/Apr/25 $$$$$$Prove;$$$${\int }_0^{\mathrm{\infty }}\frac{50x^8}{x^{20}+2x^{10}+1}dx=\varphi \pi$$$$$$ Answered by…

Question Number 219619 by Nicholas666 last updated on 29/Apr/25 $$$$$${\int }_0^{\mathrm{\infty }}{(x^2+1)}^{-1/2}dx$$$$$$ Answered by Ghisom last updated…

Question Number 219586 by Hery03 last updated on 29/Apr/25 $$Integrate:$$$$\int \frac{x^2}{\sqrt{x^2-x}+1}dx.$$ Answered by Ghisom last updated on 29/Apr/25 $$\int\frac{{x}^{\mathrm{2}} }{\:\mathrm{1}+\sqrt{{x}}\sqrt{{x}−\mathrm{1}}}{dx}=…

Question Number 219549 by Spillover last updated on 28/Apr/25 Answered by Nicholas666 last updated on 29/Apr/25 $$\int \frac{1+sinx}{1-sinx}dx=2tany-x+c$$$$\int \frac{{(1+sinx)}^2}{1-{sin}^{2}x}dx=2tany-x+c$$$$\int\frac{\mathrm{1}+\mathrm{2}\:{sin}\:{x}+{sin}^{\mathrm{2}} {x}}{{cos}^{\mathrm{2}} {x}}{dx}=\mathrm{2}\:{tan}\:{y}\:−{x}+{c}…

Question Number 219553 by Nicholas666 last updated on 28/Apr/25 $$$$$$\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} ….\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{x}_{\mathrm{1}} {x}_{\mathrm{2}} \:….{x}_{{n}} \right)}{\left(\mathrm{1}−{x}_{\mathrm{1}} \right)\left(\mathrm{1}−{x}_{\mathrm{2}} \right)….\left(\mathrm{1}−{x}_{{n}\:} \right)}\:{dx}_{\mathrm{1}}…