Question Number 46221 by Meritguide1234 last updated on 22/Oct/18 Answered by MJS last updated on 22/Oct/18 $$\mathrm{I}\:\mathrm{solved}\:\mathrm{it}\:\mathrm{but}\:\mathrm{I}'\mathrm{m}\:\mathrm{too}\:\mathrm{tired}\:\mathrm{to}\:\mathrm{type}\:\mathrm{it} \\ $$ Commented by Meritguide1234 last updated on…
Question Number 46188 by rahul 19 last updated on 22/Oct/18 $${Using}\:{dimensional}\:{analysis}\:, \\ $$$${find}\:{out}\:{value}\:{of}\:{n}\:{in}\:{given}\:{expression}: \\ $$$$\:\:\int\frac{{dx}}{\:\sqrt{\mathrm{2}{ax}−{x}^{\mathrm{2}} }}\:=\:{a}^{{n}} \mathrm{sin}^{−\mathrm{1}} \left(\frac{{x}}{{a}}\:−\mathrm{1}\right). \\ $$ Commented by rahul 19 last…
Question Number 46182 by Meritguide1234 last updated on 22/Oct/18 Commented by maxmathsup by imad last updated on 22/Oct/18 $$\:{we}\:{have}\:\mathrm{1}−{x}^{\mathrm{2}} \:+{x}^{\mathrm{4}} −….=\sum_{{n}=\mathrm{0}} ^{\infty} \left(−{x}^{\mathrm{2}} \right)^{{n}} \:=\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 111719 by mnjuly1970 last updated on 04/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:….{advanced}\:\:{mathematics}….\: \\ $$$$ \\ $$$${please}\:\:{demonstrate}\:{that}:: \\ $$$$\: \\ $$$$\Phi\:=\int_{\mathrm{0}} ^{\:\mathrm{1}} {xlog}\left(\mathrm{1}−{x}\right).{log}\left(\mathrm{1}+{x}\right)=\:\frac{\mathrm{1}}{\mathrm{4}}\:−\:{log}\left(\mathrm{2}\right)\:\:… \\ $$$$ \\…
Question Number 177241 by peter frank last updated on 02/Oct/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\left(\mathrm{x}−\mathrm{a}\right)}\mathrm{dx} \\ $$ Answered by cortano1 last updated on 02/Oct/22 $$\:\Rightarrow\mathrm{x}−\mathrm{a}=\mathrm{y}\:;\:\Rightarrow\mathrm{dx}=\mathrm{dy} \\ $$$$\mathrm{C}=\int\:\frac{\mathrm{sin}\:\left(\mathrm{a}+\mathrm{y}\right)}{\mathrm{sin}\:\mathrm{y}}\:\mathrm{dy}=\int\left(\:\mathrm{cos}\:\mathrm{a}+\mathrm{sin}\:\mathrm{a}\:\frac{\mathrm{cos}\:\mathrm{y}}{\mathrm{sin}\:\mathrm{y}}\right)\mathrm{dy} \\ $$$$\mathrm{C}=\:\left(\mathrm{x}−\mathrm{a}\right)\mathrm{cos}\:\mathrm{a}+\mathrm{sin}\:\mathrm{a}\:\int\:\frac{\mathrm{d}\left(\mathrm{sin}\:\mathrm{y}\right)}{\mathrm{sin}\:\mathrm{y}}\:…
Question Number 46171 by math khazana by abdo last updated on 22/Oct/18 $${find}\:\int\:\:\:\:\frac{{dx}}{\:\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}\:+\sqrt{{x}+\mathrm{2}}} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 22/Oct/18 $${excellent}\:{problem}… \\ $$…
Question Number 177242 by peter frank last updated on 02/Oct/22 $$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\mathrm{3x}^{\mathrm{16}} +\mathrm{5x}^{\mathrm{14}} }{\left(\mathrm{x}^{\mathrm{5}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{4}} }\mathrm{dx} \\ $$$$ \\ $$ Answered by som(math1967)…
Question Number 46156 by Meritguide1234 last updated on 21/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 21/Oct/18 $${x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1} \\ $$$$={x}^{\mathrm{2}} \left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\mathrm{2}{x}+\frac{\mathrm{2}}{{x}}−\mathrm{1}\right)…
Question Number 46129 by Necxx last updated on 21/Oct/18 Commented by Meritguide1234 last updated on 21/Oct/18 $${put}\:{x}={tan}\theta \\ $$$$\int_{\mathrm{0}} ^{\pi/\mathrm{4}} {log}\left(\mathrm{1}+{tan}\theta\right){d}\theta \\ $$$${use}\:{f}\left({a}−{x}\right)\rightarrow{f}\left({x}\right) \\ $$$${I}=\frac{\pi}{\mathrm{8}}{log}\mathrm{2}…
Question Number 177194 by peter frank last updated on 02/Oct/22 $$\int\:\:\frac{\mathrm{dx}}{\left(\mathrm{sin}\:\mathrm{x}\right)^{\frac{\mathrm{14}}{\mathrm{9}}} \left(\mathrm{cos}\:\mathrm{x}\right)^{\frac{\mathrm{4}}{\mathrm{9}}} } \\ $$ Answered by som(math1967) last updated on 02/Oct/22 $$\int\frac{{sec}^{\mathrm{2}} {xdx}}{\left({sinx}\right)^{\frac{\mathrm{14}}{\mathrm{9}}} ×\left({cosx}\right)^{\frac{\mathrm{4}}{\mathrm{9}}}…