Category: Integration

Question Number 146429 by qaz last updated on 13/Jul/21 $$\underset{\mathrm{n}=1}{\sum ^{\mathrm{\infty }}}(\mathrm{n}\cdot \ln \frac{2\mathrm{n}+1}{2\mathrm{n}-1}-1)=?$$ Commented by qaz last updated on 14/Jul/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\mathrm{n}\centerdot\mathrm{ln}\frac{\mathrm{2n}+\mathrm{1}}{\mathrm{2n}−\mathrm{1}}−\mathrm{1}\right) \…

Question Number 80846 by TawaTawa last updated on 07/Feb/20 Commented by mathmax by abdo last updated on 07/Feb/20 $${we}\:{havw}\:\int_{−\pi} ^{\pi} {costdt}\:=\mathrm{2}\int_{\mathrm{0}} ^{\pi} {cost}\:{dt}\:=\mathrm{2}\left[{sint}\right]_{\mathrm{0}} ^{\pi} =\mathrm{0}…

Question Number 80788 by Power last updated on 06/Feb/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 15235 by arnabpapu550@gmail.com last updated on 08/Jun/17 $$\int {\left(\log \sqrt{\mathrm{x}}\right)}^2\mathrm{dx}=?$$ Answered by liday last updated on 18/Jun/17 $$\int\left({log}\sqrt{{x}}\right)^{\mathrm{2}} {dx}=\frac{\mathrm{1}}{\mathrm{4}}\int\left({logx}\right)^{\mathrm{2}} {dx}=\frac{\mathrm{1}}{\mathrm{4}}\left[{x}\left({logx}\right)^{\mathrm{2}} −\int{x}\centerdot\mathrm{2}{logx}\centerdot\frac{\mathrm{1}}{{x}}{dx}\right] \…

Question Number 80764 by M±th+et£s last updated on 06/Feb/20 $$showthat$$$${\int }_0^{\mathrm{\infty }}xarctanh\left(e^{-\alpha x}\right)dx=\frac{7\zeta \left(3\right)}{8{\alpha }^2}$$ Answered by ~blr237~ last updated on 06/Feb/20…