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Category: Integration

find-arcsin-2x-1-4x-2-dx-

Question Number 45970 by maxmathsup by imad last updated on 19/Oct/18 $${find}\:\int\:\:\frac{{arcsin}\left(\mathrm{2}{x}\right)}{\:\sqrt{\mathrm{1}−\mathrm{4}{x}^{\mathrm{2}} }}{dx} \\ $$ Commented by maxmathsup by imad last updated on 20/Oct/18 $${changement}\:{arcsin}\left(\mathrm{2}{x}\right)={t}\:\:{give}\:\:\mathrm{2}{x}={sint}\:\Rightarrow\mathrm{2}{dx}={cost}\:{dt}\:\Rightarrow…

Question-176991

Question Number 176991 by mathlove last updated on 29/Sep/22 Answered by som(math1967) last updated on 29/Sep/22 $$\int\frac{{dx}}{{x}^{\mathrm{4}} +\mathrm{8}{x}^{\mathrm{2}} +\mathrm{16}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{8}}\int\frac{\mathrm{8}{dx}}{{x}^{\mathrm{4}} +\mathrm{8}{x}^{\mathrm{2}} +\mathrm{16}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{8}}\int\frac{\frac{\mathrm{8}}{{x}^{\mathrm{2}}…

please-evaluate-I-0-pi-2-1-ln-tan-x-1-1-tan-x-dx-M-N-july-1970-

Question Number 111429 by mnjuly1970 last updated on 03/Sep/20 $$\:\:\:\:\:\:{please}\:\:{evaluate}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:….\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left(\frac{\mathrm{1}}{{ln}\left({tan}\left({x}\right)\right)}\:+\:\frac{\mathrm{1}}{\mathrm{1}−{tan}\left({x}\right)}\right){dx}\:=??? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\::::\:\:\:\:\mathscr{M}.\:\mathscr{N}.{july}\:\mathrm{1970}\:::: \\ $$$$\:\: \\ $$ Answered…

Question-45885

Question Number 45885 by Meritguide1234 last updated on 17/Oct/18 Commented by maxmathsup by imad last updated on 18/Oct/18 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{n}\left(\mathrm{1}−\left({sinx}\right)^{\frac{\mathrm{1}}{{n}}} \right){dx}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:{f}_{{n}}…