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…
Question Number 138909 by bramlexs22 last updated on 19/Apr/21 $$\:\int\:\frac{\mathrm{x}^{\mathrm{6}} −\mathrm{1}}{\left(\mathrm{x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{3}} }\:\mathrm{dx}=? \\ $$ Answered by mathmax by abdo last updated on 20/Apr/21 $$\Phi=\int\:\:\frac{\mathrm{x}^{\mathrm{6}}…
Question Number 7819 by akmishra last updated on 17/Sep/16 $${let}\mathrm{2}{x}+\mathrm{1}={t} \\ $$$$\:\:\:\:{x}=\left({t}−\mathrm{1}\right)/\mathrm{2} \\ $$$${dx}={dt}/\mathrm{2} \\ $$$$\int\left({t}−\mathrm{1}\right)\sqrt{{t}}/\mathrm{2}{dt}/\mathrm{2} \\ $$$$\mathrm{1}/\mathrm{4}\int\left({t}\sqrt{{t}}−\sqrt{{t}}\right){dt} \\ $$$${continue}…..{it}.. \\ $$$$\:\: \\ $$$$ \\…
Question Number 138889 by Algoritm last updated on 19/Apr/21 Commented by MJS_new last updated on 20/Apr/21 $$\mathrm{simply}\:\mathrm{let}\:{t}=\sqrt[{\mathrm{10}}]{{x}}\:\mathrm{and}\:\mathrm{then}\:\mathrm{solve}\:\mathrm{it}. \\ $$$$\mathrm{hint}:\:{t}^{\mathrm{4}} −{t}^{\mathrm{3}} +{t}^{\mathrm{2}} −{t}+\mathrm{1}=\frac{{t}^{\mathrm{5}} +\mathrm{1}}{{t}+\mathrm{1}} \\ $$…
Question Number 7818 by akmishra last updated on 17/Sep/16 $$\int\sqrt{\mathrm{tan}\:{x}\:}{dx}=?+{k} \\ $$$$ \\ $$ Answered by prakash jain last updated on 26/Sep/16 $$\mathrm{An}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{this}\:\mathrm{question}\:\mathrm{is}\:\mathrm{present} \\ $$$$\mathrm{in}\:\mathrm{question}\:\mathrm{119}.…