Approximating definite integrals using taylor series: integral from 0 to 0.5 (dx/sqrt

[Aventura]

I can't seem to figure out the integral from 0 to 0.5 (dx/sqrt(1+x^6))... Using taylor series to approximate

 

[stapel]

I can't seem to figure out the integral from 0 to 0.5 (dx/sqrt(1+x^6))... Using taylor series to approximate

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete. Thank you!