Question Number 114699 by bemath last updated on 20/Sep/20 $$\:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{dx}}{\:\sqrt{\mathrm{1}+\mathrm{tan}\:^{\mathrm{4}} {x}}}\:? \\ $$ Commented by Dwaipayan Shikari last updated on 20/Sep/20 Answered by…
Question Number 114681 by Dwaipayan Shikari last updated on 20/Sep/20 $${Prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \frac{{x}^{{n}} }{{e}^{{x}} −\mathrm{1}}{dx}={n}!\zeta\left({n}+\mathrm{1}\right) \\ $$ Answered by mnjuly1970 last updated on 20/Sep/20 $$\:\:\:\:\:\:\:\:\:\:{proof}::…
Question Number 49144 by AdqhK ÐQeQqQ last updated on 03/Dec/18 $$\int\frac{\mathrm{1}}{{x}^{{n}} +\mathrm{1}}{dx}=?? \\ $$ Commented by MJS last updated on 04/Dec/18 $${x}^{{n}} +\mathrm{1}=\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\left({x}−\mathrm{e}^{\mathrm{i}\frac{\pi}{{n}}\left(\mathrm{2}{k}+\mathrm{1}\right)}…
Question Number 49134 by AdqhK ÐQeQqQ last updated on 03/Dec/18 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{1}/\mathrm{6}} +{x}^{\mathrm{1}/\mathrm{3}} }{dx}=?? \\ $$ Answered by arvinddayama01@gmail.com. last updated on 03/Dec/18 $${put}\:\:{x}={t}^{\mathrm{6}} \\ $$$$\:\:\:\:\:\:\:{dx}=\mathrm{6}{t}^{\mathrm{5}}…
Question Number 114671 by soumyasaha last updated on 20/Sep/20 $$ \\ $$$$\:\mathrm{Integrate}\:\:\int\:\frac{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{−\mathrm{4}} }{\mathrm{x}^{\mathrm{6}} +\mathrm{x}^{−\mathrm{6}} }\mathrm{dx} \\ $$ Answered by Olaf last updated on 20/Sep/20…
Question Number 49133 by AdqhK ÐQeQqQ last updated on 03/Dec/18 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{5}} +\mathrm{1}}{dx}=?? \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 04/Dec/18 $${pls}\:{mention}\:{the}\:{source}\:{of}\:{this}\:{intregal}… \\ $$ Answered…
Question Number 114635 by mathmax by abdo last updated on 20/Sep/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{x}^{\mathrm{4}} \mathrm{ln}\left(\mathrm{x}\right)\mathrm{ln}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx}\:\: \\ $$ Commented by mathdave last updated on 20/Sep/20…
Question Number 49094 by maxmathsup by imad last updated on 02/Dec/18 $${calculate}\:\int_{−\pi} ^{\pi} \:\:\frac{{x}^{\mathrm{2}} }{{sin}\left({sinx}\right)+\sqrt{\mathrm{1}+{sin}^{\mathrm{2}} \left({sinx}\right)}}{dx} \\ $$ Commented by Meritguide1234 last updated on 03/Dec/18…
Question Number 49032 by AdqhK ÐQeQqQ last updated on 01/Dec/18 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{3}} +\mathrm{1}}{dx}=?? \\ $$ Answered by arvinddayama01@gmail.com. last updated on 01/Dec/18 $$\int\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)}{dx}\:\:\:\:\:\:\:\because{a}^{\mathrm{3}} +{b}^{\mathrm{3}} =\left({a}+{b}\right)\left({a}^{\mathrm{2}}…
Question Number 114566 by Akeyz last updated on 19/Sep/20 Answered by mathmax by abdo last updated on 19/Sep/20 $$\mathrm{we}\:\mathrm{have}\:\prod_{\mathrm{k}=\mathrm{1}} ^{\infty} \:\mathrm{cos}\left(\frac{\mathrm{x}}{\mathrm{2}^{\mathrm{k}} }\right)\:=\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \mathrm{A}_{\mathrm{n}} \left(\mathrm{x}\right)\:\mathrm{with}\:\mathrm{A}_{\mathrm{n}} \left(\mathrm{x}\right)=\prod_{\mathrm{k}=\mathrm{1}}…