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 $$\mathrm{An}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{this}\:\mathrm{question}\:\mathrm{is}\:\mathrm{present} \\ $$$$\mathrm{in}\:\mathrm{question}\:\mathrm{119}.…
Question Number 7814 by Tawakalitu. last updated on 16/Sep/16 $$\int{x}\sqrt{\mathrm{2}{x}\:+\:\mathrm{1}}\:{dx}\: \\ $$ Commented by l-becker last updated on 17/Sep/16 $$ \\ $$$$\frac{{x}}{{dx}}\left(\sqrt{\mathrm{2}{x}+\mathrm{1}}\:\right) \\ $$$$\frac{{x}}{{dx}}\int\sqrt{\mathrm{4}{x}+\mathrm{1}}\:+{C} \\…
Question Number 73338 by mathmax by abdo last updated on 10/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{cosx}\right)}{\mathrm{3}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 73337 by mathmax by abdo last updated on 10/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({artan}\left(\mathrm{2}{x}\right)\right)}{\left(\mathrm{3}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 73336 by mathmax by abdo last updated on 10/Nov/19 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{t}} {ln}\left(\mathrm{1}+{e}^{{t}} \right){dt} \\ $$ Commented by mathmax by abdo last updated…
Question Number 7798 by Tawakalitu. last updated on 16/Sep/16 $$\int\frac{{x}^{\mathrm{2}} }{\:\sqrt{{x}^{\mathrm{3}} \:+\:\mathrm{5}}}\:{dx} \\ $$ Commented by sou1618 last updated on 16/Sep/16 $$\frac{{d}}{{dx}}\left(\sqrt{{x}^{\mathrm{3}} +\mathrm{5}}\right)=\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}\sqrt{{x}^{\mathrm{3}} +\mathrm{5}}}…
Question Number 73335 by mathmax by abdo last updated on 10/Nov/19 $${eplcit}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}+{t}+{t}^{\mathrm{2}} \right){dt}\:\:\:\:\:\:{with}\:{x}>\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({t}^{\mathrm{2}} \:+{t}\:+\sqrt{\mathrm{2}}\right){dt} \\ $$ Commented by mathmax…