Approximate an integral using Taylor/Maclaurin series

[professordad]

Please give only hints, no full solutions :)

Homework Statement

Use series to approximate the definite integral to within the indicated accuracy:
\int_0^{0.1} \frac{dx}{\sqrt{1 + x^3}}, |\text{error}| < 10^{-8}

Homework Equations

Taylor series and Maclaurin series

The Attempt at a Solution

This doesn't seem to match or bear resemblance to any of the "famous" ones which can easily be expressed with series e^x, \sin{x}, \cos{x}, and I tried taking seven derivatives, but this is awfully annoying. Are there any other methods?

Thanks.

 

[LCKurtz]

Try expanding $(1+x^3)^{-1/2}$ as a binomial series.