Question Number 112699 by bemath last updated on 09/Sep/20 $$\:\left(\mathrm{1}\right)\:\int\:\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{e}^{\sqrt{\mathrm{cos}\:\mathrm{x}}} }{\:\sqrt{\mathrm{cos}\:\mathrm{x}}}\:\mathrm{dx}\: \\ $$$$\:\left(\mathrm{2}\right)\:\frac{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{2A}}}{\mathrm{1}−\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{2A}}}??\: \\ $$$$\left(\mathrm{3}\right)\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{b}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} \right)} \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 112666 by bemath last updated on 09/Sep/20 $$\int\:\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{x}+\mathrm{1}}}\right)\:\mathrm{dx}\:? \\ $$ Answered by Her_Majesty last updated on 09/Sep/20 $${by}\:{parts} \\ $$$${u}'=\mathrm{1}\:\Rightarrow\:{u}={x} \\ $$$${v}={tan}^{−\mathrm{1}}…
Question Number 47120 by math solver by abdo. last updated on 05/Nov/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} {e}^{−{t}} {ln}\left(\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} \right){dt} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 47119 by math solver by abdo. last updated on 05/Nov/18 $${let}\:{u}_{{n}} =\int_{−\infty} ^{\infty} \:{e}^{−{nx}^{\mathrm{2}} +{x}} {dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{u}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:\sum_{{n}} \:{u}_{{n}} \\ $$…
Question Number 47114 by maxmathsup by imad last updated on 04/Nov/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\left({x}^{\mathrm{2}} −\mathrm{1}\right){ln}\left({x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{2}{x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1}\right)}{dx} \\ $$ Commented by maxmathsup by imad last…
Question Number 47112 by maxmathsup by imad last updated on 04/Nov/18 $${calculate}\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({cosx}+{sinx}\right){ex} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 05/Nov/18 Commented by…
Question Number 47101 by Meritguide1234 last updated on 04/Nov/18 Commented by tanmay.chaudhury50@gmail.com last updated on 05/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 05/Nov/18 $$\int\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}}…
Question Number 47098 by rahul 19 last updated on 04/Nov/18 $${prove}\:{that}:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \left(\mathrm{1}+\frac{{t}}{{n}}\right)^{{n}} {dt}\:=\:{e}−\frac{\mathrm{1}}{{e}}. \\ $$ Commented by rahul 19 last updated on 04/Nov/18…
Question Number 47088 by Meritguide1234 last updated on 04/Nov/18 Answered by MJS last updated on 04/Nov/18 $${x}^{\mathrm{2}} +{ax}+{b}=\mathrm{0} \\ $$$${x}=−\frac{{a}}{\mathrm{2}}\pm\frac{\sqrt{{a}^{\mathrm{2}} −\mathrm{4}{b}}}{\mathrm{2}}\:\Rightarrow\:\alpha=−\frac{{a}}{\mathrm{2}}−\frac{\sqrt{{a}^{\mathrm{2}} −\mathrm{4}{b}}}{\mathrm{2}};\:\beta=−\frac{{a}}{\mathrm{2}}+\frac{\sqrt{{a}^{\mathrm{2}} −\mathrm{4}{b}}}{\mathrm{2}\left(\right.} \\ $$$${bx}^{\mathrm{2}}…
Question Number 112613 by mnjuly1970 last updated on 08/Sep/20 $$\:\:\:\:\:….{number}\:{theory}… \\ $$$$\:\:\:\:\:\:\:{Question}\::\:\:\:\:\:\:\mathrm{I}{f}\:\:\:{a}\:,\:{b}\:,\:{c}\:\:\in\:\mathbb{N}\:\:\:;\:{then}\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}!\ast{b}!\ast{c}!\mid\left({a}+{b}+{c}\right)!\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}\:.\:{july}\:\mathrm{970}# \\…