Category: Integration

Question Number 62453 by Tawa1 last updated on 21/Jun/19 $$\int \frac{\mathrm{x}}{{\mathrm{e}}^{\mathrm{x}}-1}\mathrm{dx},\mathrm{for}\mathrm{x}>0$$ Commented by mathmax by abdo last updated on 21/Jun/19 $$\int\:\:\frac{{x}}{{e}^{{x}} −\mathrm{1}}{dx}\:=\int\:\:\frac{{x}\:{e}^{−{x}} }{\mathrm{1}−{e}^{−{x}}…

Question Number 62437 by mathsolverby Abdo last updated on 21/Jun/19 $$letf\left(x\right)={\int }_0^1\frac{arctan(1+xt)}{t^2+1}dt$$$$determineaexplicitformforf\left(x\right)$$$$2)calculate{\int }_0^1\frac{arctan(1+2t)}{1+t^2}dt$$$$$$…

Question Number 62420 by mathsolverby Abdo last updated on 20/Jun/19 $$let{u}_n\left(x\right)=\frac{1}{n^x}-{\int }_n^{n+1}\frac{dt}{t^x}withx\in [1,2]$$$$1)provethat0⩽u_n\left(x\right)⩽\frac{1}{n^x}-\frac{1}{{(n+1)}^x}(n>0)$$$$\left.\mathrm{2}\right){prove}\:{that}\:\Sigma\:{u}_{{n}} \left({x}\right){converges} \…

Question Number 62418 by mathmax by abdo last updated on 20/Jun/19 $$calculate{\int }_0^1\mathrm{\Gamma }\left(t\right).\mathrm{\Gamma }(1-t)dt$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 127952 by rs4089 last updated on 03/Jan/21 Answered by Ar Brandon last updated on 03/Jan/21 $$\Psi=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}^{\mathrm{2}} \sqrt{\frac{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}\mathrm{dx}=\int_{\mathrm{0}} ^{\mathrm{1}} \left\{\frac{\mathrm{x}^{\mathrm{2}}…