Ok, so my function is $\displaystyle f(x)=\frac{1}{(1+x^2)^{1/3}}$ and I'm supposed to approximate the integral for it. I can do that once I have the power series easily enough since the instructions are to get a sixth-degree Taylor polynomial, which I can do if I know the power series, and then it's just a matter of plug and chug....now, I can do the derivatives for this and find the pattern, but it'll get extremely ugly after the first derivative, so is there a way to use an elementary power series on this problem so I can avoid having to do the 2nd, 3rd, etc. derivatives by parts?