Menu Close

Category: Integration

Advanced-Calculus-find-the-value-of-the-infinite-series-n-1-1-n-1-H-2n-2n-1-

Question Number 140885 by mnjuly1970 last updated on 13/May/21 $$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:…….\:{Advanced}\:::::::::::\bigstar\bigstar\bigstar::::::::::\:{Calculus}……. \\ $$$$\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}\:\:{the}\:{infinite}\:{series}:: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\Theta\::=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \mathrm{H}_{\:\mathrm{2}{n}} }{\mathrm{2}{n}−\mathrm{1}}\:=\:??? \\ $$$$\:\:\:\:\:\:\:\:\:\:…….\mathscr{M}.\mathscr{N}.{july}.\mathrm{1970}…….. \\…

0-1-ln-2-ln-1-x-2-1-x-dx-

Question Number 140866 by liberty last updated on 13/May/21 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{ln}\:\mathrm{2}−\mathrm{ln}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{1}−\mathrm{x}}\:\mathrm{dx}\:=?\: \\ $$ Answered by mindispower last updated on 15/May/21 $$=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\int_{\mathrm{0}} ^{{x}}…

Determine-whether-the-improper-integral-converges-or-diverges-1-2x-7-7x-3-5x-2-1-dx-

Question Number 140823 by liberty last updated on 13/May/21 $$\mathrm{Determine}\:\mathrm{whether}\:\mathrm{the}\:\mathrm{improper} \\ $$$$\mathrm{integral}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverges}\: \\ $$$$\int_{\mathrm{1}} ^{\:\infty} \:\frac{\mathrm{2x}+\mathrm{7}}{\mathrm{7x}^{\mathrm{3}} +\mathrm{5x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{dx}\: \\ $$ Commented by liberty last updated…

Question-75248

Question Number 75248 by cesar.marval.larez@gmail.com last updated on 08/Dec/19 Commented by mathmax by abdo last updated on 14/Dec/19 $$\frac{{d}}{{dx}}\left(\frac{{e}^{{x}} }{\mathrm{1}+{x}}\right)\:=\frac{{e}^{{x}} \left(\mathrm{1}+{x}\right)−{e}^{{x}} ×\mathrm{1}}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2}} }\:=\frac{\mathrm{xe}^{\mathrm{x}} }{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2}} }\:\Rightarrow…