Question Number 108593 by Rasikh last updated on 18/Aug/20 Answered by Her_Majesty last updated on 18/Aug/20 $$\left(−\mathrm{1}\right)^{{x}} ={e}^{{xln}\left(−\mathrm{1}\right)} ={e}^{{i}\pi{x}} ={cos}\pi{x}+{isin}\pi{x} \\ $$$$\Rightarrow\:\int\left(−\mathrm{1}\right)^{{x}} {dx}=\frac{\mathrm{1}}{\pi}\left({sin}\pi{x}−{icos}\pi{x}\right)+{C} \\ $$…
Question Number 108584 by mathmax by abdo last updated on 17/Aug/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}+\mathrm{2}}\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 108582 by mathmax by abdo last updated on 17/Aug/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Answered by mnjuly1970 last updated on 18/Aug/20 $$\mathrm{x}=\mathrm{tan}\left(\mathrm{t}\right)\Rightarrow\:\Omega=\int_{\mathrm{0}}…
Question Number 174117 by Mathspace last updated on 25/Jul/22 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{dx}}{\mathrm{1}+{x}^{{n}} }\:{interms}\:{of} \\ $$$$\psi\:\left({digamma}\right) \\ $$ Answered by Mathspace last updated on 25/Jul/22 $$\int_{\mathrm{0}}…
Question Number 174118 by Mathspace last updated on 25/Jul/22 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}}\:{by}\:{using} \\ $$$$\psi\:\:\left({digamma}\right) \\ $$ Answered by mnjuly1970 last updated on 25/Jul/22 $$\:\:\:\underset{{n}=\mathrm{1}}…
Question Number 108583 by mathmax by abdo last updated on 17/Aug/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by mnjuly1970 last updated on 18/Aug/20…
Question Number 108573 by mnjuly1970 last updated on 17/Aug/20 $$\:\:\:\:\:\:\:\:\:\mathrm{please}:\:\:\:\mathrm{in}\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\:\frac{{cos}\left(\mathrm{A}\right)}{{sin}\left(\mathrm{B}\right){sin}\left(\mathrm{C}\right)}\:+\frac{{cos}\left(\mathrm{B}\right)}{{sin}\left(\mathrm{A}\right){sin}\left(\mathrm{C}\right)}+\frac{{cos}\left(\mathrm{C}\right)}{{sin}\left(\mathrm{A}\right){sin}\left(\mathrm{B}\right)}\:=\mathrm{2}\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by veth last updated on…
Question Number 174096 by mnjuly1970 last updated on 24/Jul/22 $$ \\ $$$$\:\:\:{f}\left({x}\right)=\:{ax}^{\:\mathrm{2}} +\:{bx}\:+{c}\:\:{is}\:{given} \\ $$$$\:\:\:\:\:\:{a}\:\neq\:{b}\:\neq\:{c}\:\:,\:{a}\:,\:{b}\:,\:{c}\:\in\:\mathbb{R}\: \\ $$$$\:\:\:\:\:\:\:{a}\neq\mathrm{0}\:\:\:{and}\:\:\:: \\ $$$$\:\:\:\:\:\:\:\:{f}\left({ax}\:+\:{b}\:\right)={f}\:\left({bx}\:+\:{c}\right) \\ $$$$\:\:\:\:\:\:{find}\::\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\left({f}\left({b}\right)\:\:−\:{f}\left({a}\:\right)\right)=? \\ $$ Answered by…
Question Number 43027 by Raj Singh last updated on 06/Sep/18 Commented by math khazana by abdo last updated on 07/Sep/18 $${let}\:{I}\:=\:\int\:\:\:\frac{{x}^{\mathrm{2}} \:+\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}−\mathrm{2}\right)}{dx}\:{let}\:{decompose} \\ $$$${F}\left({x}\right)=\frac{{x}^{\mathrm{2}}…
Question Number 43008 by MJS last updated on 06/Sep/18 $$\left({y}'\right)^{\mathrm{2}} =−\mathrm{1}+\mathrm{sin}\:{x} \\ $$$${y}=? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18 $$\frac{{dy}}{{dx}}=\sqrt{−\mathrm{1}+{sinx}}\: \\ $$$$\frac{{dy}}{{dx}}=\sqrt{−\mathrm{1}\left(\mathrm{1}−{sinx}\right)}\:…