Question Number 51188 by Abdo msup. last updated on 24/Dec/18 $${find}\:\:\int\:\:\:\:\:\frac{{cos}^{\mathrm{2}} {x}}{{cosx}\:+\mathrm{2}{sinx}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 51186 by Abdo msup. last updated on 24/Dec/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\left[{nx}\right]}{\mathrm{2}{x}+\mathrm{1}}{dx} \\ $$ Commented by Abdo msup. last updated on 25/Dec/18 $${let}\:{A}_{{n}} =\int_{\mathrm{0}}…
Question Number 116717 by Yamadeu last updated on 06/Oct/20 $$\int{xdx} \\ $$ Answered by MJS_new last updated on 06/Oct/20 $$=\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+{C} \\ $$ Answered by…
Question Number 116710 by ravisoni505 last updated on 06/Oct/20 Answered by maths mind last updated on 06/Oct/20 $${case}\:{one}\:{a}=\mathrm{0} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2}{a}} {x}^{{n}} \sqrt{\mathrm{2}{ax}−{x}^{\mathrm{2}} }{dx}=\mathrm{0} \\…
Question Number 182242 by mathlove last updated on 06/Dec/22 $$\underset{\mathrm{0}} {\int}^{\mathrm{2}} \underset{\mathrm{0}} {\int}^{\mathrm{3}} \underset{\mathrm{0}} {\int}^{\mathrm{4}} {e}^{{x}+{y}+{z}} \:{dx}\:{dy}\:{dz}=? \\ $$ Answered by Ar Brandon last updated…
Question Number 182238 by HeferH last updated on 06/Dec/22 Answered by Acem last updated on 06/Dec/22 $${a}=\mathrm{5}\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{sin}\:{x}}{{x}}\:{dx}=\:\:\:\frac{\mathrm{5}\pi}{\mathrm{2}} \\ $$$$ \\ $$$${XD} \\ $$…
Question Number 116701 by bemath last updated on 06/Oct/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{x}+\mathrm{x}\sqrt{\mathrm{x}}}\:=? \\ $$ Commented by bobhans last updated on 06/Oct/20 $$\:\int\:\frac{\mathrm{dx}}{\mathrm{x}+\mathrm{x}\sqrt{\mathrm{x}}\:}\:=\:\int\:\frac{\mathrm{dx}}{\mathrm{x}\left(\mathrm{1}+\sqrt{\mathrm{x}}\:\right)} \\ $$$$\left[\:\mathrm{letting}\:\mathrm{x}\:=\:\lambda^{\mathrm{2}} \:\rightarrow\mathrm{dx}\:=\:\mathrm{2}\lambda\:\mathrm{d}\lambda\:\right]\: \\ $$$$\mathrm{I}=\int\:\frac{\mathrm{2}\lambda\:\mathrm{d}\lambda}{\lambda^{\mathrm{2}}…
Question Number 116687 by megrex last updated on 05/Oct/20 $${Help}\:{please},\:{to}\:{solve}\:{this}\:… \\ $$$${If}\:{f}\left({x}\right)=\mathrm{1}+{x}^{\mathrm{2}} \:\:{for}\:{x}\in\left[−\mathrm{2},\mathrm{2}\right]\:{and}\: \\ $$$$\:\:\:\:\:\:{f}\left({x}\right)=\mathrm{5}\:\:\:\:\:\:\:\:{otherwise}. \\ $$$${Then}\:{what}\:{is}\:{the}\:{value}\:{of} \\ $$$$\int_{−\mathrm{2}} ^{+\mathrm{2}} {f}\left(\mathrm{2}{x}^{\mathrm{2}} \right){dx}? \\ $$$$ \\…
Question Number 116672 by mnjuly1970 last updated on 05/Oct/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\:\:{nice}\:\:{calculus}\:… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{\pi}{\mathrm{4}}\:\:−\mathscr{A}{rctan}\left({x}\right)\right)\frac{{dx}}{\mathrm{1}−{x}^{\mathrm{2}} }\:=\:\frac{\mathrm{G}}{\mathrm{2}}\:\:\checkmark\:\:\:\: \\ $$$$\:\:\:\:\:\:\: \\ $$$$\mathrm{G}\:{is}\:\:\:{catalan}\:\:{constant}\:……
Question Number 116667 by mnjuly1970 last updated on 05/Oct/20 $$\:\:\:\:\:\:\:\:\:\:\:\:…\:\:\:{nice}\:\:{calculus}… \\ $$$$ \\ $$$$\:\:\:\:\:\:{very}\:{nice}\:\:{integral}:: \\ $$$$\:\:\:\:\:\:\:{demonstrate}::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}−{x}}{\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} \right){log}\left({x}\right)}\:{dx}\overset{???} {=}{log}\left(\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}\right)…