Question Number 42370 by Raj Singh last updated on 24/Aug/18 Commented by maxmathsup by imad last updated on 24/Aug/18 $${let}\:{A}\:=\:\int\:\:\:\frac{{dx}}{{sin}\left(\mathrm{2}{x}\right)+{sinx}} \\ $$$${A}\:=\:\int\:\:\:\:\:\frac{{dx}}{\mathrm{2}{sinx}\:{cosx}\:+{sinx}}\:=\:\int\:\:\:\:\:\:\frac{{sinx}}{\mathrm{2}{sin}^{\mathrm{2}} {xcosx}\:+{sin}^{\mathrm{2}} {x}}\:{dx} \\…
Question Number 42374 by maxmathsup by imad last updated on 24/Aug/18 $${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:{arctan}\left({xt}^{\mathrm{2}} \right){cos}\left({t}^{\mathrm{2}} \right)\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicite}\:{form}\:{of}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{explicite}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:{cos}\left({t}^{\mathrm{2}}…
Question Number 42366 by Joel578 last updated on 24/Aug/18 $$\underset{\mathrm{2005}} {\overset{\mathrm{2017}} {\int}}\:\frac{\left(\mathrm{ln}\:\mid{x}\:−\:\mathrm{2017}\mid\right)^{\mathrm{2017}} }{\left(\mathrm{ln}\:\mid{x}\:−\:\mathrm{2015}\mid\right)^{\mathrm{2017}} \:+\:\left(\mathrm{ln}\:\mid{x}\:−\:\mathrm{2017}\mid\right)^{\mathrm{2017}} }\:{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 24/Aug/18 $$\int_{{a}}…
Question Number 42358 by Tawa1 last updated on 24/Aug/18 $$\int_{\:−\mathrm{1}} ^{\:\mathrm{1}} \:\frac{\mathrm{x}^{\mathrm{2015}} }{\:\sqrt[{\mathrm{2015}}]{\mathrm{1}\:+\:\mathrm{x}}\:\:+\:\:\sqrt[{\mathrm{2015}}]{\mathrm{1}\:−\:\mathrm{x}}\:}\:\:\mathrm{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 24/Aug/18 $$\Upsilon\left({x}\right)=\frac{{x}^{\mathrm{2015}} }{\left(\mathrm{1}+{x}\right)^{\frac{\mathrm{1}}{\mathrm{2015}}} +\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{1}}{\mathrm{2015}}}…
Question Number 42364 by Tawa1 last updated on 24/Aug/18 $$\int\:\:\frac{\mathrm{x}\:+\:\mathrm{sinx}\:−\:\mathrm{cosx}\:−\:\mathrm{1}}{\mathrm{x}\:+\:\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{sinx}}\:\mathrm{dx} \\ $$ Commented by maxmathsup by imad last updated on 24/Aug/18 $${I}\:=\:\int\:\frac{{x}+{e}^{{x}} \:+{sinx}\:−{e}^{{x}} −{cosx}\:−\mathrm{1}}{{x}+{e}^{{x}}…
Question Number 173424 by mnjuly1970 last updated on 11/Jul/22 $$ \\ $$$$\:\:\:\:\mathrm{prove}\:\:\mathrm{that} \\ $$$$ \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{sinh}\left(\mathrm{x}\right)}\:\mathrm{dx}\:=\:\frac{\pi}{\mathrm{2}}\mathrm{tanh}\left(\frac{\pi}{\mathrm{2}}\right) \\ $$$$ \\ $$ Answered by Mathspace…
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Question Number 42336 by maxmathsup by imad last updated on 23/Aug/18 $${find}\:\:\int\:{ln}\left({x}−{cosx}\right){dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 107858 by mathmax by abdo last updated on 13/Aug/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\mathrm{dx} \\ $$ Commented by mathdave last updated on 13/Aug/20…
Question Number 107859 by mathmax by abdo last updated on 13/Aug/20 $$\mathrm{find}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{x}^{\mathrm{n}} \sqrt{\mathrm{1}+\mathrm{x}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\:\left(\mathrm{n}\:\mathrm{natural}\right) \\ $$ Terms of Service Privacy Policy Contact:…