Menu Close

Category: Integration

let-f-x-ln-1-2x-x-2-1-1-calculste-f-n-x-and-f-n-0-2-develop-f-at-integr-serie-3-find-0-1-f-x-dx-

Question Number 124922 by mathmax by abdo last updated on 07/Dec/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{2x}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculste}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{develop}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$…

sinx-3-dx-

Question Number 124906 by Mammadli last updated on 06/Dec/20 $$\int\boldsymbol{{sinx}}^{\mathrm{3}} \boldsymbol{{dx}}=? \\ $$ Commented by Dwaipayan Shikari last updated on 06/Dec/20 $$\int{sinx}^{\mathrm{3}} {dx}\:\:\:\:\:\:\:\:\:\: \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}{i}}\int{e}^{{ix}^{\mathrm{3}}…

Question-124903

Question Number 124903 by Algoritm last updated on 06/Dec/20 Answered by MJS_new last updated on 06/Dec/20 $$\mathrm{just}\:\mathrm{decompose}\:\mathrm{and}\:\mathrm{solve},\:\mathrm{no}\:\mathrm{special} \\ $$$$\mathrm{knowledge}\:\mathrm{necessary}.\:\mathrm{the}\:\mathrm{answer}\:\mathrm{is}: \\ $$$$\frac{{x}−\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}+\frac{\mathrm{1}}{\mathrm{4}}\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)\:−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid{x}+\mathrm{1}\mid\:+{C} \\ $$$$\mathrm{now}\:\mathrm{try}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{this}\:\mathrm{for}\:\mathrm{yourself}…