Question Number 67019 by mathmax by abdo last updated on 21/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}^{\mathrm{2}} } {arctan}\left({x}^{\mathrm{2}} \right){dx}\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 67017 by mathmax by abdo last updated on 21/Aug/19 $${find}\:\int\:\:{arctan}\left(\mathrm{1}+\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$ Commented by mathmax by abdo last updated on 24/Aug/19 $${let}\:{I}\:=\int\:{arctan}\left(\mathrm{1}+\sqrt{{x}+\mathrm{1}}\right){dx}\:\:{changement}\:\sqrt{{x}+\mathrm{1}}={t}\:{give}\:{x}+\mathrm{1}={t}^{\mathrm{2}} \:\Rightarrow…
Question Number 67016 by mathmax by abdo last updated on 21/Aug/19 $${find}\:\int\:{arctan}\left(\mathrm{1}+\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 67012 by mathmax by abdo last updated on 21/Aug/19 $${find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{arctan}\left(\left[{x}\right]\right)}{{x}^{\mathrm{3}} }{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 67008 by mathmax by abdo last updated on 21/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dt}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{3}}…
Question Number 67011 by mathmax by abdo last updated on 21/Aug/19 $${calculate}\:{U}_{{n}} =\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{arctan}\left({n}\left[{x}\right]\right)}{{x}^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 67006 by mathmax by abdo last updated on 21/Aug/19 $${calculae}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} }\:\:\:{with}\:{n}\:{integr}\:{natural}\:{and}\:{n}>\mathrm{0} \\ $$ Commented by mathmax by abdo last…
Question Number 67005 by mathmax by abdo last updated on 21/Aug/19 $${find}\:\int\:\:\:\frac{{x}−\mathrm{2}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}+\mathrm{2}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx} \\ $$ Commented by mathmax by abdo last updated on 27/Aug/19…
Question Number 132534 by liberty last updated on 15/Feb/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}\:\:\rightarrow\mathrm{diverges}\:\mathrm{or}\:\mathrm{converges}? \\ $$ Commented by MJS_new last updated on 15/Feb/21 $$\mathrm{we}\:\mathrm{only}\:\mathrm{want}\:\mathrm{to}\:\mathrm{know}\:\mathrm{if}\:\mathrm{it}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{not} \\ $$$$\mathrm{0}\leqslant{x}\leqslant\frac{\pi}{\mathrm{2}}\:\Rightarrow\:\frac{\mathrm{1}}{\mathrm{2}}\leqslant\frac{\mathrm{1}}{\mathrm{1}+\mathrm{sin}\:{x}}\leqslant\mathrm{1}\:\Rightarrow\:\mathrm{converges} \\…
Question Number 132519 by mnjuly1970 last updated on 14/Feb/21 $$\:\:\:\:\:….\:\:{nice}\:\:{calculus}…. \\ $$$$\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {ln}\left({n}\right)}{{n}}=\gamma{ln}\left(\mathrm{2}\right)−\frac{\mathrm{1}}{\mathrm{2}}{ln}^{\mathrm{2}} \left(\mathrm{2}\right) \\ $$$$ \\ $$ Answered by mindispower…