Question Number 49252 by cesar.marval.larez@gmail.com last updated on 04/Dec/18 Answered by kaivan.ahmadi last updated on 05/Dec/18 $$\bigstar\mathrm{b} \\ $$$$\mathrm{f}'\left(\mathrm{x}\right)=\mathrm{2tg}\left(\mathrm{sec}\left(\mathrm{cos5x}−\mathrm{3}\right)\right)\left(\mathrm{1}+\mathrm{tg}^{\mathrm{2}} \left(\mathrm{sec}\left(\mathrm{cos}\left(\mathrm{5x}−\mathrm{3}\right)\right)\right)\right)\left(\mathrm{sec}\left(\mathrm{cos}\left(\mathrm{5x}−\mathrm{3}\right)\right)\right)^{'} = \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{other}\:\mathrm{hand} \\ $$$$\left(\mathrm{sec}\left(\mathrm{cos}\left(\mathrm{5x}−\mathrm{3}\right)\right)\right)'=\mathrm{sec}\left(\mathrm{cos}\left(\mathrm{5x}−\mathrm{3}\right)\right)\mathrm{tg}\left(\mathrm{cos}\left(\mathrm{5x}−\mathrm{3}\right)\right).\left(−\mathrm{5sin}\left(\mathrm{5x}−\mathrm{3}\right)\right)…
Question Number 49250 by cesar.marval.larez@gmail.com last updated on 04/Dec/18 $${Apply}\:{derivative}\:{criteria} \\ $$$${F}\left({x}\right)={x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 05/Dec/18 $$\frac{{dF}\left({x}\right)}{{dx}}=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{10}{x}−\mathrm{2}…
Question Number 114773 by soumyasaha last updated on 21/Sep/20 $$\: \\ $$$$\:\:\mathrm{Evaluate}:\:\:\int\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{5}} \mathrm{x}\:+\:\mathrm{cos}^{\mathrm{5}} \mathrm{x}}\:\mathrm{dx} \\ $$ Answered by MJS_new last updated on 21/Sep/20 $$\int\frac{{dx}}{\mathrm{sin}^{\mathrm{5}} \:{x}\:+\mathrm{cos}^{\mathrm{5}}…
Question Number 49232 by Abdo msup. last updated on 04/Dec/18 $${let}\:{f}\left({a}\right)=\:\int_{−\infty} ^{+\infty} {cos}\left({x}^{\mathrm{2}} \:+{ax}\:+\mathrm{1}\right){dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}\left({a}\right)\:{and}\:{f}^{'} \left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{f}^{\left({n}\right)} \left({a}\right)\: \\ $$ Commented by Abdo…
Question Number 49225 by AdqhK ÐQeQqQ last updated on 04/Dec/18 $$\int\frac{\mathrm{1}}{{z}\left({z}^{\mathrm{17}} +\mathrm{1}\right)}=??\:{find}\:{please} \\ $$ Answered by arvinddayama01@gmail.com. last updated on 04/Dec/18 $$\int\frac{\mathrm{1}}{{z}\left({z}^{\mathrm{17}} +\mathrm{1}\right)}.\frac{{z}^{\mathrm{16}} }{{z}^{\mathrm{16}} }{dz}…
Question Number 49187 by Rahul kharade last updated on 04/Dec/18 $$\int\frac{{sinx}}{{sin}\mathrm{4}{x}}{dx} \\ $$$$ \\ $$ Answered by MJS last updated on 04/Dec/18 $$\int\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:\mathrm{4}{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\:\rightarrow\:{dx}=\frac{\mathrm{2}{dt}}{{t}^{\mathrm{2}}…
Question Number 114699 by bemath last updated on 20/Sep/20 $$\:\:\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}}…