Question Number 138970 by mathmax by abdo last updated on 20/Apr/21 $$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\:\frac{\mathrm{xsin}\left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated…
Question Number 138971 by mathmax by abdo last updated on 20/Apr/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73429 by Henri Boucatchou last updated on 12/Nov/19 $$\:\:\:{Solve}\::\:\int\frac{\left[{cos}^{−\mathrm{1}} {x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right]^{−\mathrm{1}} }{{log}_{{e}} \left[\mathrm{2}+\frac{{sin}\left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)}{\pi}\right]}{dx} \\ $$$$\:\:{Evaluate}\:\:\int_{−\pi/\mathrm{2}} ^{\:\pi/\mathrm{2}} {sin}^{\mathrm{2}} {xcos}^{\mathrm{2}} {x}\left({cosx}+{sinx}\right){dx} \\ $$ Commented…
Question Number 73428 by Learner-123 last updated on 12/Nov/19 $${Evaluate}\:: \\ $$$$\left.\mathrm{1}\right)\:\int_{−\mathrm{2}} ^{\:\mathrm{2}} \int_{−\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }} ^{\:\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }} \:\left(\mathrm{3}−{x}\right){dydx}\:. \\ $$$$\left({after}\:{changing}\:{the}\:{integral}\:{to}\:{polar}\:{form}\right). \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\mathrm{4}}…
Question Number 138967 by mnjuly1970 last updated on 20/Apr/21 $$\:\Theta=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}\right).{log}^{\mathrm{2}} \left({x}\right)}{{x}}{dx}=\frac{\pi}{\mathrm{24}}\left(\mathrm{12}\:\gamma^{\:\mathrm{2}} +\pi^{\mathrm{2}} \right)….\checkmark \\ $$ Answered by Dwaipayan Shikari last updated on 20/Apr/21…
Question Number 7880 by tawakalitu last updated on 22/Sep/16 $$\int\left(\sqrt{\mathrm{1}\:−\:{x}\:−\:{x}^{\mathrm{2}} }\right)\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7872 by tawakalitu last updated on 22/Sep/16 $$\int\frac{{x}\:−\:\mathrm{8}}{{x}^{\mathrm{2}} \:+\:\mathrm{4}{x}\:+\:\mathrm{16}}\:{dx} \\ $$ Commented by prakash jain last updated on 23/Sep/16 $$\frac{{x}−\mathrm{8}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{16}}=\frac{{x}−\mathrm{8}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{4}+\mathrm{12}} \\…
Question Number 138940 by mnjuly1970 last updated on 20/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{mathematics}.. \\ $$$${prove}\:{that}: \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{arctan}\left({x}\right).{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:\:=\frac{\pi^{\mathrm{2}} {ln}\left(\mathrm{2}\right)}{\mathrm{4}}+\frac{\mathrm{7}}{\mathrm{8}}\:\zeta\left(\mathrm{3}\right) \\ $$ Terms of…
Question Number 138933 by mnjuly1970 last updated on 20/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73397 by mathmax by abdo last updated on 11/Nov/19 $${find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{t}} {ln}\left(\mathrm{1}−{xt}^{\mathrm{2}} \right){dt}\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{t}} {ln}\left(\mathrm{1}−\frac{{t}^{\mathrm{2}} }{\mathrm{2}}\right){dt} \\ $$ Commented…