# Power Series Problem

• Apr 19th 2009, 02:31 PM
zhupolongjoe
Power Series Problem
How can I represent integral from 0 to 1 of 2/(3x^4+16) dx as the sum of an infinite series?

Thanks.
• Apr 19th 2009, 02:52 PM
skeeter
Quote:

Originally Posted by zhupolongjoe
How can I represent integral from 0 to 1 of 2/(3x^4+16) dx as the sum of an infinite series?

Thanks.

$\frac{2}{3x^4 + 16} =$

$\frac{2}{16 - (-3x^4)} =$

$\frac{2}{16} \cdot \frac{1}{1 - \left(-\frac{3x^4}{16}\right)} =$

$\frac{1}{8}\left(1 - \frac{3x^4}{2^4} + \frac{3^2 x^8}{2^8} - \frac{3^3 x^{12}}{2^{12}} + ...\right)$

I'll leave the definite integral to you ...