I was given the following problem:

A. Use Derive to evaluate the integral $\displaystyle \int x^5*(x^2+1)^{1/2} dx$

B. Use integration tables in the back of your book to evaluate the integral from part A. State the table entry used and show all work. After you find this antiderivative by hand, show that it is equal to the antiderivative given by derive.

While using derive, I obtained this as the answer for part A:

= $\displaystyle \frac{(x^2+1)^{1/2}(15x^6+3x^4-4x^2+8)}{105}$

But using my Ti-89 I got this instead:

= $\displaystyle \frac{(x^2+1)^{3/2}(15x^4-12x^2+8)}{105}$

So I'm not sure what's going on there, but I went ahead and tried out an integration table that looked useful:

$\displaystyle \int u^n(bu+a)^{1/2} du = \frac{2}{b(2n+3)}(u^n(a+bu)^{3/2} - na \int u^{n-1}(bu+a)^{1/2} du$

However, when I use u=x, n=5 and b=x the integral at the end looks just as messy as what I started with. Do I really have to use the integration table again on the last integral part of the integration table? Am I doing it wrong?

Edit: I found an online pdf of the integration tables I have access to at this site: http://teachers.sduhsd.k12.ca.us/abr...lesStewart.pdf