Question Number 136399 by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{calculate}\:\int\:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{n}} \sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136381 by mnjuly1970 last updated on 21/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:……{sdvanced}\:\:\:{cslculus}…… \\ $$$$\:{if}\:\:{x}\in\mathbb{R}^{+} \:{and}::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}\left({x}\right)=\int_{\mathrm{0}} ^{\:{x}} \frac{{e}^{{t}} −\mathrm{1}}{{t}}{ln}\left(\frac{{x}}{{t}}\right){dt} \\ $$$$\:\:{then}\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\Psi=\int_{\mathrm{0}} ^{\:\infty} {e}^{−{x}} \boldsymbol{\phi}\left({x}\right){dx}=\zeta\left(\mathrm{2}\right)…
Question Number 70842 by oyemi kemewari last updated on 08/Oct/19 Commented by oyemi kemewari last updated on 08/Oct/19 please explain line 9 to 10 Terms of Service Privacy Policy Contact:…
Question Number 136365 by liberty last updated on 21/Mar/21 $$\int\:\frac{{dx}}{\mathrm{sin}\:{x}\:\sqrt{\mathrm{cos}\:{x}}}\:=? \\ $$ Answered by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{I}\:=\int\:\frac{\mathrm{dx}}{\mathrm{sinx}\sqrt{\mathrm{cosx}}}\:\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{cosx}=\mathrm{t}^{\mathrm{2}} \:\Rightarrow\mathrm{x}=\mathrm{arcos}\left(\mathrm{t}^{\mathrm{2}} \right) \\…
Question Number 70818 by oyemi kemewari last updated on 08/Oct/19 $$\mathrm{what}\:\mathrm{the}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{a}+\mathrm{b}−\mathrm{x}\right)\:\mathrm{dx} \\ $$ Commented by kaivan.ahmadi last updated on…
Question Number 5278 by sara last updated on 04/May/16 $$\int\left\{\left(\mathrm{3}{x}\right){i}+\left(\mathrm{2}{x}\right){y}\right\}{dx}= \\ $$$$ \\ $$ Answered by FilupSmith last updated on 04/May/16 $$\int\left(\mathrm{3}{xi}+\mathrm{2}{xy}\right){dx} \\ $$$$=\mathrm{3}{i}\int{xdx}+\mathrm{2}{y}\int{xdx} \\…
Question Number 70808 by rajesh4661kumar@gmail.com last updated on 08/Oct/19 Answered by MJS last updated on 08/Oct/19 $$\int\left(\mathrm{sec}\:{x}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} \left(\mathrm{csc}\:{x}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} {dx}=\int\frac{{dx}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}\:\left(\mathrm{tan}\:{x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} }= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:{x}\:\rightarrow\:{dx}=\left(\mathrm{cos}\:{x}\right)^{\mathrm{2}} {dt}\right] \\ $$$$=\int\frac{{dt}}{{t}^{\frac{\mathrm{4}}{\mathrm{3}}}…
Question Number 5266 by Kasih last updated on 03/May/16 $$\int\:\frac{\mathrm{3}{x}}{\:\sqrt{{x}^{\mathrm{2}} +\:\mathrm{2}{x}+\:\mathrm{5}}}\:{dx} \\ $$ Commented by prakash jain last updated on 03/May/16 $$\mathrm{You}\:\mathrm{can}\:\mathrm{integrate}\:\mathrm{as}\:\mathrm{following} \\ $$$$\frac{\mathrm{3}{x}+\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}}}−\frac{\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 136343 by snipers237 last updated on 21/Mar/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{{x}^{\mathrm{2021}} }{{x}−{ln}\left(\underset{{k}=\mathrm{0}} {\overset{\mathrm{2020}} {\sum}}\frac{{x}^{{k}} }{{k}!}\right)}\:\overset{?} {=}\:\mathrm{2021}!\: \\ $$ Answered by mindispower last updated on 21/Mar/21…
Question Number 136333 by Bird last updated on 20/Mar/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{t}^{{a}} }{\mathrm{1}+{t}+{t}^{\mathrm{2}} }{dt} \\ $$$${study}\:{first}\:{the}\:{convergence} \\ $$$$\left({a}\:{real}\right) \\ $$ Terms of Service Privacy Policy…