course Mth 174
I believe that I get it now. But just to be certain let me know if I did the following the right.It is # 13 in the book the problem is x(x^2 + 3)^2:
I let u = x^2 + 3 then du = 2x dx then xdx = 1/2 du. So you have 1/2 * (u)^2. that will turn into 1/2(u^2/2)
1/2 u^2 could be expressed as u^2 / 2, but not as 1/2 u^2 / 2.
That will be 1/2 * (x^2 +3)^3 / 3 or 1/6(x^2 + 3)^3
That is correct.
Think of integrating 1/2 u^2 to get 1/2 * u^3 / 3, which is 1/6 u^3. Then after integrating the u expression, substitute x^2 + 3 for u.