Solutions - 0230-04

(a)

$$\begin{array}{c}\frac{1}{1+x^4}\gg \gg \frac{1}{1-(-x^4)}\gg \gg \sum _{n=0}^{\infty }{(-x^4)}^n\\ \\ \gg \gg \sum _{n=0}^{\infty }{(-1)}^n{x}^{4n}\end{array}$$

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(b)

$$\int \frac{1}{1+x^4}dx=\int \sum _{n=0}^{\infty }{(-1)}^n{x}^{4n}dx\gg \gg C+\sum _{n=0}^{\infty }{(-1)}^n\frac{1}{4n+1}{x}^{4n+1}$$