Category: Integration

Question Number 134795 by 0731619177 last updated on 07/Mar/21 Answered by EDWIN88 last updated on 07/Mar/21 $$\mathrm{noting}\mathrm{that}\mathrm{the}\mathrm{integrand}\mathrm{is}\mathrm{even}\mathrm{function}$$$$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:\left(\pi\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{\infty} \frac{\mathrm{sin}\:\left(\pi\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{dx}…

Question Number 69257 by Henri Boucatchou last updated on 21/Sep/19 $${\int }_{-2}^4\mid \mathit{x}{\mid }^{2{\mathit{x}}^3}\mathit{d}\mathit{x}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 69241 by ~ À ® @ 237 ~ last updated on 21/Sep/19 $$LetconsiderK={\int }_0^1\frac{(1-x^a)(1-x^b)(1-x^c)}{(x-1)lnx}dx$$$$provethat$$$${e}^{{K}} =\:\frac{\left({a}+{b}\right)!\left({a}+{c}\right)!\left({b}+{c}\right)!}{{a}!{b}!{c}!\left({a}+{b}+{c}\right)!}\:\:…

Question Number 69233 by ~ À ® @ 237 ~ last updated on 21/Sep/19 $$ProvethatB={\int }_0^1{\left[ln(-lnu)\right]}^{2}du={\gamma }^2+\zeta \left(2\right)$$ Commented by mathmax by…

Question Number 69231 by ~ À ® @ 237 ~ last updated on 21/Sep/19 $$Provethat\underset{p=0}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^p}{4p+1}=\frac{\pi -argcoth\left(\sqrt{2}\right)}{4\sqrt{2}}and$$$$\underset{p=0}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^p}{4p+3}=\frac{\pi +argcoth\left(\sqrt{2}\right)}{4\sqrt{2}}$$…