Category: Integration

Question Number 130598 by Lordose last updated on 27/Jan/21 $${\int }_0^{\mathrm{\infty }}\frac{{\mathrm{x}}^2{\tan }^{-1}\left(\mathrm{x}\right)}{1+{\mathrm{x}}^6}\mathrm{dx}$$ Answered by mindispower last updated on 27/Jan/21 $$=\frac{\mathrm{1}}{\mathrm{3}}\int_{\mathrm{0}}…

Question Number 65061 by mathmax by abdo last updated on 24/Jul/19 $$letf\left(x\right)={\int }_0^{\mathrm{\infty }}\frac{dt}{{(x-t+t^2)}^3}withx>\frac{1}{4}$$$$1)calculatef\left(x\right)$$$$\left.\mathrm{2}\right)\:{calculate}\:{also}\:\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dt}}{\left({x}−{t}+{t}^{\mathrm{2}} \right)^{\mathrm{4}} } \…

Question Number 130560 by rs4089 last updated on 26/Jan/21 Answered by Dwaipayan Shikari last updated on 26/Jan/21 $$\frac{\pi }{2(r+r^3+r^6+r^{10}+\dots .)}$$ Answered by…

Question Number 65015 by aliesam last updated on 24/Jul/19 $$\int \frac{\sqrt{x+1}-\sqrt{x-1}}{\sqrt{x+1}+\sqrt{x-1}}dx$$ Commented by mathmax by abdo last updated on 24/Jul/19 $$letI=\int \frac{\sqrt{x+1}-\sqrt{x-1}}{\sqrt{x+1}+\sqrt{x-1}}dx\Rightarrow I=\int \frac{{(\sqrt{x+1}-\sqrt{x-1})}^2}{x+1-x+1}dx$$$$=\frac{\mathrm{1}}{\mathrm{2}}\:\int\:\left({x}+\mathrm{1}−\mathrm{2}\sqrt{{x}^{\mathrm{2}}…

Question Number 65003 by mathmax by abdo last updated on 24/Jul/19 $$find{\int }_0^{\mathrm{\infty }}\frac{dx}{\mathrm{\Gamma }\left(x\right)}with\mathrm{\Gamma }\left(x\right)={\int }_0^{\mathrm{\infty }}{t}^{x-1}{e}^{-t}dt(x>0)$$ Terms of Service Privacy Policy…