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Find the Taylor Series About x=0x = 0 For the Indefinite Integral

Question 19

Multiple Choice

Find the Taylor series about x=0x = 0 for the indefinite integral x15x2dx\int \frac { x } { 1 - 5 x ^ { 2 } } d x


A) n=052n2nx2n\sum _ { n = 0 } ^ { \infty } \frac { 5 ^ { 2 n } } { 2 n } x ^ { 2 n }
B) n=05n2n+2x2n+2\sum _ { n = 0 } ^ { \infty } \frac { 5 ^ { n } } { 2 n + 2 } x ^ { 2 n + 2 }
C) n=05n2nx2n\sum _ { n = 0 } ^ { \infty } \frac { 5 ^ { n } } { 2 n } x ^ { 2 n }
D) n=05n2n+1x2n+1\sum _ { n = 0 } ^ { \infty } \frac { 5 ^ { n } } { 2 n + 1 } x ^ { 2 n + 1 }

Correct Answer:

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