Finding the integral of an improper fraction

  • Thread starter Thread starter howsockgothap
  • Start date Start date
  • Tags Tags
    Fraction Integral
howsockgothap
Messages
59
Reaction score
0

Homework Statement



Use substitution to find the integral of (12x2 + X -12)/(3x - 2)


Homework Equations





The Attempt at a Solution



I know I need to use long division to work it down to a proper fraction. That is where my real problem lies. Using long division I get that (12x2+x-12)/(3x-2) is equal to 4x-3 with a remainder of -6. I don't really understand what that means in terms of my question, especially with the remainder. Does this just mean that I have to find the integral of (4x-3) - 6/(3x-2)?
 
Physics news on Phys.org
howsockgothap said:
Does this just mean that I have to find the integral of (4x-3) - 6/(3x-2)?

Yes, assuming that your long division is correct. You should know how to take the integral of (4x-3) - 6/(3x-2).
 
right on, thanks.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

Similar threads

Replies
10
Views
2K
Replies
25
Views
2K
Replies
15
Views
1K
Replies
6
Views
2K
Replies
44
Views
5K
Replies
8
Views
2K
Replies
5
Views
1K
Back
Top