Question Number 76664 by aliesam last updated on 29/Dec/19 $$\int_{\mathrm{0}} ^{+\infty} \frac{{t}\:{ln}\left({t}\right)}{\left({t}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:{dt} \\ $$ Commented by mathmax by abdo last updated on 29/Dec/19…
Question Number 76663 by aliesam last updated on 29/Dec/19 Answered by benjo 1/2 santuyy last updated on 29/Dec/19 $$\mathrm{2}^{\mathrm{3}{n}\:} \:? \\ $$ Answered by mind…
Question Number 76661 by john santu last updated on 29/Dec/19 $${calculate}\:\int\:\frac{{x}^{\mathrm{2}} −\mathrm{2}}{\left({x}^{\mathrm{4}} +\mathrm{5}{x}^{\mathrm{2}} +\mathrm{4}\right)\:{arc}\mathrm{tan}\:\left(\frac{{x}^{\mathrm{2}} +\mathrm{2}}{{x}}\right)}\:{dx}\: \\ $$ Answered by benjo 1/2 santuyy last updated on…
Question Number 76657 by Tony Lin last updated on 29/Dec/19 $${prove}\:{that}\:{sin}^{−\mathrm{1}} \left({tanhx}\right)={tan}^{−\mathrm{1}} \left({sinhx}\right) \\ $$ Answered by john santu last updated on 29/Dec/19 $$\left(\mathrm{1}\right)\:\mathrm{tan}\:{hx}\:=\:\mathrm{sin}\:{y} \\…
Question Number 142191 by iloveisrael last updated on 27/May/21 Commented by Mathspace last updated on 27/May/21 $${why}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={i}+\frac{\mathrm{2}{i}}{\mathrm{1}+{e}^{{ix}} }\:? \\ $$$${and}\:{what}\:{is}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{sin}\left({nx}\right)}{\mathrm{1}+{e}^{{ix}} }{dx} \\ $$$${all}\:{this}\:{need}\:{proof}……
Question Number 142185 by mohammad17 last updated on 27/May/21 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$ Answered by MJS_new last updated on 27/May/21 $$\mathrm{I}\:\mathrm{showed}\:\mathrm{this}\:\mathrm{before}… \\ $$$${x}^{\mathrm{4}} +\mathrm{1}=\left({x}^{\mathrm{2}} −\sqrt{\mathrm{2}}{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}}…
Question Number 76650 by john santu last updated on 29/Dec/19 $${two}\:{dice}\:{are}\:{tossed}\:{together}\:\mathrm{4}\:{times}. \\ $$$${the}\:{odds}\:{appear}\:{that}\:{the}\:{number}\: \\ $$$${on}\:{the}\:{first}\:{dice}\:{us}\:{twice}\:{the}\:{number} \\ $$$${on}\:{the}\:{second}\:{dice}\:{exactly}\:{twice}\:? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 76651 by john santu last updated on 29/Dec/19 $${if}\:{a}\:{and}\:{b}\:{two}\:{numbers}\:{do}\:{not}\:{have}\: \\ $$$${to}\:{be}\:{chosen}\:{randomly}\:{and}\:{with}\: \\ $$$${returns}\:{from}\:{the}\:{set}\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\}.\:{what}\: \\ $$$${probability}\:{that}\:\frac{{a}}{{b}}\:{is}\:{an}\:{integer}\:? \\ $$ Answered by benjo 1/2 santuyy last…
Question Number 11114 by ABD last updated on 12/Mar/17 Answered by ajfour last updated on 12/Mar/17 Commented by ajfour last updated on 12/Mar/17 $$\frac{{AB}}{{BC}}=\frac{\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta}\:\Rightarrow{BC}=\frac{\mathrm{4cos}\:\theta}{\mathrm{sin}\:\theta} \\…
Question Number 76645 by naka3546 last updated on 29/Dec/19 Commented by mr W last updated on 29/Dec/19 $$\left(\mathrm{5}−{a}\right)^{\mathrm{2}} ={a}^{\mathrm{2}} +\left(\mathrm{3}+{a}\right)^{\mathrm{2}} \\ $$$${a}^{\mathrm{2}} +\mathrm{16}{a}−\mathrm{16}=\mathrm{0} \\ $$$$\Rightarrow{a}=\mathrm{4}\sqrt{\mathrm{5}}−\mathrm{8}=\mathrm{2}\left(\mathrm{2}\sqrt{\mathrm{5}}−\mathrm{4}\right)…