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Math Help - Power Series Problem

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by zhupolongjoe View Post
    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 ...
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