Question Number 7932 by tawakalitu last updated on 24/Sep/16 Commented by sou1618 last updated on 25/Sep/16 $${set}\:\:{f}\left({x}\right)=\frac{{sinx}}{\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} } \\ $$$${f}\left(−{x}\right)=\frac{{sin}\left(−{x}\right)}{\mathrm{1}+\left(−{x}\right)^{\mathrm{2}} +\left(−{x}\right)^{\mathrm{4}} }=−{f}\left({x}\right) \\ $$$${so}…
Question Number 138994 by mathlove last updated on 21/Apr/21 Answered by qaz last updated on 21/Apr/21 $$\int\frac{{dx}}{{xln}\left({x}\right){ln}\left({lnx}\right)}=\int\frac{{d}\left({lnx}\right)}{{ln}\left({x}\right){ln}\left({lnx}\right)}=\int\frac{{d}\left({ln}\left({lnx}\right)\right)}{{ln}\left({lnx}\right)}={ln}\left({ln}\left({lnx}\right)\right)+{C} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 138993 by bramlexs22 last updated on 21/Apr/21 $$\int\:\sqrt{\mathrm{x}+\sqrt{\mathrm{x}−\sqrt{\mathrm{x}+\sqrt{\mathrm{x}−\sqrt{\mathrm{x}+\sqrt{\mathrm{x}−\sqrt{\mathrm{x}+…}}}}}}}\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 138972 by mathmax by abdo last updated on 20/Apr/21 $$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 138973 by mathmax by abdo last updated on 20/Apr/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty\:} \:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} −\mathrm{x}^{\mathrm{2}} +\mathrm{2}} \\ $$ Answered by mathmax by abdo last updated…
Question Number 7898 by tawakalitu last updated on 23/Sep/16 $$\int{cos}^{\mathrm{6}} {x}\:\:{dx} \\ $$ Commented by sandy_suhendra last updated on 24/Sep/16 $${cos}^{\mathrm{6}} {x}\:=\:\left({cos}^{\mathrm{2}} {x}\right)^{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}{cos}\mathrm{2}{x}\right)^{\mathrm{3}}…
Question Number 138970 by mathmax by abdo last updated on 20/Apr/21 $$\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}}…