# Thread: Last Taylor series question for awhile, promise

1. ## Last Taylor series question for awhile, promise

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?

2. What you have to do here it is to use for $\displaystyle |x|<1,\,(1+x)^\alpha=\sum_{k\,=\,0}^\infty\binom{\ alpha}{k}x^k$ where $\displaystyle \binom{\alpha}{k}=\frac{\alpha(\alpha-1)(\alpha-2)\cdots(\alpha-k+1)}{k!}.$

3. ## But in this case

doesnt it need to be $\displaystyle (1+x^2)^\alpha$?