A question about Taylor series expansions

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The Taylor series expansion for the function f(x) = x * e^(-x^2) about x = -1 is derived as follows: -(1/E) - (x + 1)/E + (x + 1)^2/E + (5 (x + 1)^3)/(3 E) + (x + 1)^4/(6 E) - (23 (x + 1)^5)/(30 E) - (29 (x + 1)^6)/(90 E) + (103 (x + 1)^7)/(630 E). This expansion was computed using Mathematica, which provides a systematic approach to obtaining Taylor series. Understanding the derivation process is essential for mastering series expansions in calculus.

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Find the Taylor series expansions for f(x)=x*e^(-x^2) about x = -1
-(1/E) - (x + 1)/E + (x + 1)^2/E + (5 (x + 1)^3)/(3 E) + (x + 1)^4/(
6 E) - (23 (x + 1)^5)/(30 E) - (29 (x + 1)^6)/(90 E) + (
103 (x + 1)^7)/(630 E)...
This is the answer from Mathematica but i don't know how it goes.
Can anybody help me?
Thanks.
 
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