Question Number 128346 by Ahmed1hamouda last updated on 06/Jan/21 Answered by MJS_new last updated on 06/Jan/21 $$\int{x}^{\mathrm{2}} \sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{2}{x}+\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}\:\rightarrow\:{dx}=\frac{\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}}{\mathrm{2}\left(\mathrm{2}{x}+\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}\right)}{dt}\right] \\…
Question Number 62806 by mathmax by abdo last updated on 25/Jun/19 $${find}\:{the}\:{value}\:{of}\:\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}+\mathrm{1}}{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$ Commented by mathmax by abdo last…
Question Number 62808 by mathmax by abdo last updated on 25/Jun/19 $${f}\left({t}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{e}^{−{xt}} }{\left({x}+{t}\right)^{\mathrm{2}} }{dx}\:\:\:\:{with}\:{t}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{set}\:{of}\:{definition}\:{for}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{continuity}\:{of}\:{f} \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{derivability}\:{of}\:{f} \\ $$$$\left.\mathrm{4}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\…
Question Number 62805 by mathmax by abdo last updated on 25/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left(\:{x}^{\mathrm{2}} −\mathrm{2}{i}\right)^{\mathrm{2}} }\:{dx} \\ $$ Commented by mathmax by abdo…
Question Number 128334 by liberty last updated on 06/Jan/21 $$\Omega\:=\:\int\:\frac{\mathrm{x}^{\mathrm{2}} }{\:\sqrt{\left(\mathrm{a}+\mathrm{bx}^{\mathrm{2}} \right)^{\mathrm{5}} }}\:\mathrm{dx}\:;\:\mathrm{where}\::\:\mathrm{a};\:\mathrm{b}\:>\mathrm{0}\: \\ $$ Answered by bramlexs22 last updated on 06/Jan/21 $$\Omega\:=\:\int\:\frac{{x}^{\mathrm{2}} }{\left({a}+{bx}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}}…
Question Number 62790 by Tawa1 last updated on 25/Jun/19 Commented by Tawa1 last updated on 25/Jun/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral} \\ $$ Answered by MJS last updated on…
Question Number 128316 by mnjuly1970 last updated on 08/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:{nice}\:\:{calculus} \\ $$$$\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\mathrm{3}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx}=? \\ $$$$ \\ $$ Answered by mindispower last updated…
Question Number 62781 by Tawa1 last updated on 25/Jun/19 $$\int\:\mathrm{sec}\left(\mathrm{2x}\right)\:\mathrm{e}^{\mathrm{2x}} \:\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128285 by john_santu last updated on 06/Jan/21 $$\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{7}}\right)−\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:=? \\ $$ Answered by liberty last updated on 06/Jan/21 $$\:\mathrm{let}\:\varphi\:=\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{7}}\right)−\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right) \\ $$$$\:\varphi\:=\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{7}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{5}\pi}{\mathrm{7}}\right) \\ $$$$\:\Rightarrow\mathrm{2}\varphi\mathrm{sin}\:\mathrm{t}\:=\:\mathrm{2sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{t}\:+\:\mathrm{2sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{3t}+\mathrm{2sin}\:\mathrm{tcos}\:\mathrm{5t} \\…
Question Number 128276 by john_santu last updated on 06/Jan/21 $$\:\int_{{e}^{\mathrm{2}} } ^{\:\infty} \:\frac{{dx}}{{x}^{\mathrm{3}} \:\mathrm{ln}\:{x}}\:? \\ $$ Answered by liberty last updated on 06/Jan/21 $$\:\digamma\:=\:\underset{\mathrm{Y}\rightarrow+\infty} {\mathrm{lim}}\int_{\mathrm{e}^{\mathrm{2}}…