Question Number 116196 by mnjuly1970 last updated on 01/Oct/20 $$\:\:\:\:\:{please}\:{solve}\:: \\ $$$$\:\:\: \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} {tan}^{\mathrm{9}} \left({x}\right){dx}\:=??? \\ $$ Answered by mindispower last updated on…
Question Number 50659 by rahul 19 last updated on 18/Dec/18 $$\int_{\mathrm{0}\:} ^{\:\infty} \:\frac{{dx}}{\mathrm{4}−{x}^{\mathrm{2}} }\:=\:? \\ $$ Commented by maxmathsup by imad last updated on 18/Dec/18…
Question Number 50633 by Necxx last updated on 18/Dec/18 $${please}\:{help}\:{integrate}\:\frac{{x}+\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}}{dx} \\ $$ Commented by maxmathsup by imad last updated on 18/Dec/18 $${let}\:{I}\:=\:\int\:\:\frac{{x}+{sinx}}{\mathrm{1}+{cosx}}{dx}\:\:{we}\:{have}\:{I}\:=\int\:\:\frac{{x}}{\mathrm{1}+{cosx}}{dx}\:+\int\:\:\frac{{sinx}}{\mathrm{1}+{cosx}}{dx}\:{but} \\ $$$$\int\:\:\frac{{sinx}}{\mathrm{1}+{cosx}}{dx}\:=\int\:\frac{−{d}\left({cosx}\right)}{\mathrm{1}+{cosx}}\:{dx}=−{ln}\mid\mathrm{1}+{cosx}\mid\:+{c}_{\mathrm{1}} \\…
Question Number 116162 by mnjuly1970 last updated on 01/Oct/20 $$\:\: \\ $$$$ \\ $$$$\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{16}^{{n}} \left({n}^{\mathrm{2}} +\mathrm{3}{n}+\mathrm{2}\right)}\:\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}^{\mathrm{2}} \:=\frac{\mathrm{8}}{\mathrm{3}\pi}\: \\ $$$$ \\ $$$${m}.{n}.{july}\:\mathrm{1970}. \\ $$$$\:…
Question Number 116123 by Henri Boucatchou last updated on 01/Oct/20 $$ \\ $$$$\mathrm{Study}\:\mathrm{according}\:\mathrm{to}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{real}\:\alpha\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{integral}\:\:\int_{\alpha} ^{+\infty} \frac{{ln}\mid{x}\mid}{\:\sqrt[{\mathrm{3}}]{{x}\left({x}+\mathrm{1}\right)}}{dx} \\ $$ Terms of Service Privacy…
Question Number 116112 by Lordose last updated on 01/Oct/20 $$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\int_{\:\mathrm{0}} ^{\:\infty} \frac{\boldsymbol{\mathrm{lnx}}}{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}\:=\:\mathrm{0} \\ $$$$ \\ $$ Answered by MJS_new last updated on…
Question Number 181643 by Frix last updated on 28/Nov/22 $$\Omega=\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\mathrm{tan}^{−\mathrm{1}} \:\mathrm{cos}\:{x}\:{dx} \\ $$$$\left(\mathrm{I}'\mathrm{d}\:\mathrm{need}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{if}\:\mathrm{possible}.\:\mathrm{I}'\mathrm{ve}\right. \\ $$$$\left.\mathrm{got}\:\mathrm{no}\:\mathrm{idea}\:\mathrm{if}\:\mathrm{and}\:\mathrm{how}\:\mathrm{this}\:\mathrm{can}\:\mathrm{be}\:\mathrm{solved}.\right) \\ $$ Commented by MJS_new last updated on…
Question Number 116096 by mathmax by abdo last updated on 30/Sep/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\mathrm{x}^{\mathrm{2}} −\mathrm{i}}\mathrm{dx}\:\:\:\:\:\left(\mathrm{i}=\sqrt{−\mathrm{1}}\right) \\ $$ Answered by mindispower last updated on 01/Oct/20 $${let}\:{f}\left({z}\right)=\frac{{ln}\left({z}\right)}{{z}^{\mathrm{2}}…
Question Number 116098 by mathmax by abdo last updated on 30/Sep/20 $$\left.\mathrm{1}\right)\mathrm{calculate}\:\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{\mathrm{d}\theta}{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}\:\mathrm{cos}\theta\:+\mathrm{1}}\:\:\:\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\mathrm{explicite}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{\mathrm{cos}\theta}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{d}\theta \\ $$ Terms of…
Question Number 116097 by mathmax by abdo last updated on 30/Sep/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\mathrm{x}^{\mathrm{4}} \:+\mathrm{1}}\mathrm{dx}\: \\ $$ Answered by mnjuly1970 last updated on 01/Oct/20 $$\:\:{solution}:\:\:\:\Omega=\int_{\mathrm{0}}…