Question Number 51876 by Tinkutara last updated on 31/Dec/18 Commented by maxmathsup by imad last updated on 31/Dec/18 $${let}\:{solve}\:{y}^{'} \:+\mathrm{2}{y}\:={f}\left({x}\right)\:\:\left({e}\right) \\ $$$$\left({he}\right)\:\Rightarrow{y}^{'} \:+\mathrm{2}{y}\:=\mathrm{0}\:\Rightarrow\frac{{y}^{'} }{{y}}=−\mathrm{2}\:\:\Rightarrow{ln}\left({y}\right)=−\mathrm{2}{x}\:+{k}\:\:\Rightarrow{y}\left({x}\right)={C}\:{e}^{−\mathrm{2}{x}} \\…
Question Number 117409 by hatakekakashi1729gmailcom last updated on 11/Oct/20 Answered by Lordose last updated on 10/Dec/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 117403 by bemath last updated on 11/Oct/20 $$\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\left(\mathrm{arc}\:\mathrm{tan}\:\mathrm{x}\right)^{\mathrm{2}} \:\mathrm{dx}\:=? \\ $$ Commented by MJS_new last updated on 11/Oct/20 $$\mathrm{use}\:\mathrm{arctan}\:{x}\:=\frac{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{i}{x}\right)\:−\mathrm{ln}\:\left(\mathrm{1}−\mathrm{i}{x}\right)}{\mathrm{2i}}\:\Rightarrow \\ $$$$−\frac{\mathrm{1}}{\mathrm{4}}\underset{\mathrm{0}}…
Question Number 117396 by mnjuly1970 last updated on 11/Oct/20 $$\:\:\:\:\:\:\:\:…{differential}\:\:{equation}…\: \\ $$$$ \\ $$$$\:\:\:\:{solve}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{{dy}}{{dx}}=\frac{\mathrm{1}}{{xy}+\mathrm{2}{x}^{\mathrm{2}} {y}} \\ $$$$\:\:\:\:\:\:\:\:\:{general}\:\:{solution}\:=??? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$\:…
Question Number 117380 by mnjuly1970 last updated on 11/Oct/20 $$\:\:\:\:\:\:\:\:\:\:\:…\:\:{prove}\:\:{that}\:… \\ $$$$\:\: \\ $$$$\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}{sin}\left(\pi^{\mathrm{2}} {x}+\frac{\mathrm{1}}{{x}}\right){dx}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{8}\pi}} \\ $$$$ \\ $$$$\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$ Commented by…
Question Number 51841 by wishyman last updated on 31/Dec/18 Commented by wishyman last updated on 31/Dec/18 $${Happy}\:{new}\:{year}\:\mathrm{2019}\:{from}\:{wishyman} \\ $$ Commented by Abdo msup. last updated…
Question Number 51834 by Abdo msup. last updated on 31/Dec/18 $${calculatef}\left({a}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left(\mathrm{1}+{at}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}\:\:{with}\:{a}>\mathrm{0}. \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{3}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}. \\ $$ Commented by…
Question Number 182902 by Tawa11 last updated on 16/Dec/22 $$\int\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} \:\:\boldsymbol{\mathrm{dx}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 51825 by Abdo msup. last updated on 30/Dec/18 $${find}\:{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{e}^{−\alpha} {x}\right){dx}\:\:{with}\:\alpha\geqslant\mathrm{0} \\ $$ Commented by maxmathsup by imad last updated on 31/Dec/18…
Question Number 51824 by Abdo msup. last updated on 30/Dec/18 $${find}\:\int\:\:\:\frac{{dx}}{{cosx}\:+{cos}\left(\mathrm{2}{x}\right)+{cos}\left(\mathrm{3}{x}\right)} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 31/Dec/18 $$\int\frac{{dx}}{{cos}\mathrm{2}{x}+\mathrm{2}{cos}\mathrm{2}{x}.{cosx}} \\ $$$$\int\frac{{dx}}{{cos}\mathrm{2}{x}\left(\mathrm{1}+\mathrm{2}{cosx}\right)} \\ $$$$\int\frac{{dx}}{\left(\mathrm{2}{cos}^{\mathrm{2}}…