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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
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
$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{2x}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculste}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{develop}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

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