Question Number 139928 by qaz last updated on 02/May/21 $${prove}::\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} {ln}\left(\frac{\mathrm{5}}{\mathrm{4}}+\mathrm{sin}\:{x}\right){dx}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 74394 by aliesam last updated on 23/Nov/19 Commented by mathmax by abdo last updated on 23/Nov/19 $$\left.\mathrm{1}\right)\:{let}\:{decompose}\:{F}\left({x}\right)=\frac{\mathrm{4}{x}^{\mathrm{2}} +{x}}{{x}^{\mathrm{3}} −\mathrm{81}{x}}\:\Rightarrow{F}\left({x}\right)=\frac{\mathrm{4}{x}^{\mathrm{2}} +{x}}{{x}\left({x}−\mathrm{9}\right)\left({x}+\mathrm{9}\right)} \\ $$$$=\frac{\mathrm{4}{x}+\mathrm{1}}{\left({x}−\mathrm{9}\right)\left({x}+\mathrm{9}\right)}\:=\frac{{a}}{{x}−\mathrm{9}}\:+\frac{{b}}{{x}+\mathrm{9}} \\…
Question Number 74395 by mathmax by abdo last updated on 23/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:{e}^{−\mathrm{2}{x}} \left[{e}^{{x}} \right]{dx} \\ $$ Commented by ~blr237~ last updated on 23/Nov/19…
Question Number 8853 by FilupSmith last updated on 01/Nov/16 $$\int_{\mathrm{0}} ^{\:{n}} \left(\left({x}+\mathrm{1}\right)^{\mathrm{1}/{x}} −\mathrm{1}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 139912 by mnjuly1970 last updated on 02/May/21 $$ \\ $$$$\:\:\:\:\:{prove}\:{that}::\: \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\Omega}\::=\int_{\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{2}}} \frac{{dx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:={log}\left(\varphi\right) \\ $$$$\:\:\:\:\:\:\:\:\varphi:={golden}\:{ratio}\:… \\ $$$$ \\ $$ Answered by…
Question Number 74367 by Learner-123 last updated on 23/Nov/19 $${Solve}\:: \\ $$$$\left({D}^{\mathrm{4}} +\mathrm{4}\right){y}=\mathrm{0}\: \\ $$$${given}:\:{y}\left(\mathrm{0}\right)=\mathrm{0}\:,\:{y}'\left(\mathrm{0}\right)=\mathrm{2}\:,\:{y}''\left(\mathrm{0}\right)=\mathrm{0}\:{and} \\ $$$${y}'''\left(\mathrm{0}\right)=\mathrm{4}. \\ $$ Commented by mr W last updated…
Question Number 139889 by qaz last updated on 02/May/21 $$\int_{\mathrm{0}} ^{\mathrm{4}} \frac{\mathrm{tan}^{−\mathrm{1}} {x}}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}}{dx}=? \\ $$ Commented by qaz last updated on 02/May/21 $${I}=\int_{\mathrm{0}} ^{\mathrm{4}}…
Question Number 74348 by mathmax by abdo last updated on 22/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left({sin}\left({x}^{\mathrm{2}} \right)\right)}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 74346 by mathmax by abdo last updated on 22/Nov/19 $${find}\:\int\:\:\frac{{x}+\sqrt{{x}+\mathrm{1}}}{\mathrm{2}\sqrt{{x}−\mathrm{1}}+\mathrm{3}}{dx} \\ $$ Answered by MJS last updated on 24/Nov/19 $$\int\frac{{x}+\sqrt{{x}+\mathrm{1}}}{\mathrm{3}+\mathrm{2}\sqrt{{x}−\mathrm{1}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{2}\sqrt{{x}−\mathrm{1}}\:\rightarrow\:{dx}=\sqrt{{x}−\mathrm{1}}{dt}\right] \\…
Question Number 74349 by mathmax by abdo last updated on 22/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left(\mathrm{2}\pi{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by abdomathmax last updated on 23/Nov/19…