Category: Integration

Question Number 171971 by ilhamQ last updated on 22/Jun/22 $$\int \frac{x}{x^2+4x+3}dx=\dots$$ Answered by cortano1 last updated on 22/Jun/22 $$\frac{x}{(x+1)(x+3)}=\frac{a}{x+1}+\frac{b}{x+3}$$$$a=\frac{-1}{-1+3}=-\frac{1}{2}$$$$\:{b}=\frac{−\mathrm{3}}{−\mathrm{3}+\mathrm{1}}\:=\:\frac{\mathrm{3}}{\mathrm{2}}…

Question Number 40893 by abdo.msup.com last updated on 28/Jul/18 $$let{u}_k=1-{(1-\frac{1}{2^k})}^{n-1}$$$$1)provethat\mathrm{\Sigma }{u}_{k}converges$$$$2)letf\left(x\right)=1-{(1-\frac{1}{2^x})}^{n-1}withx⩾0$$$$provethat\mathrm{\forall }p\in N$$$$\sum_{{k}=\mathrm{1}} ^{{p}+\mathrm{1}} \:{u}_{{k}}…

Question Number 40890 by abdo.msup.com last updated on 28/Jul/18 $$1)calculate{\int }_{\frac{1}{n+1}}^{\frac{1}{n}}[\frac{1}{t}-\left[\frac{1}{t}\right]]dt$$$$2)provethat{\int }_0^1[\frac{1}{t}-\left[\frac{1}{t}\right]]dt=1-\gamma$$$$\gamma isconstantnumberofeuler$$ Commented by maxmathsup by imad…

Question Number 40888 by prof Abdo imad last updated on 28/Jul/18 $$provethat\mathrm{\forall }\xi \in ]0,\pi [$$$$\mid {\int }_{\xi }^{\pi }{\left(\frac{sint}{t}\right)}^{n}dt\mid ⩽\pi {\left(\frac{sin\xi }{\xi }\right)}^{n}nintegrnatural$$ Terms of Service Privacy Policy…

Question Number 40887 by prof Abdo imad last updated on 28/Jul/18 $$calculate{\int }_0^1\frac{tln\left(t\right)}{t^2-1}dt$$ Commented by prof Abdo imad last updated on…