Integrating Partial Fractions: x^2+2x-1/2x^3+3x^2-2x (x>1/2)

[oyala]

Hi guys I have a question here relating integration by partial praction..


the question said what is the antiderivative of

x^2+2x-1/2x^3 +3x^2 - 2x

valid only when x > 1/2.

anyway i had poor background in math and working hard to catch up...
I don't understant why "valid only when x > 1/2".
if you integrate that indefinte integral when do you have to do to make sure relate x>1/2

 

[grindfreak]

While the function certainly exists for many points less than 1/2, it is not continuous over the interval -inf<x<1/2 since it has three singularities (I'll let you solve for these). Thus it is best to define the domain of the function as 1/2<x<inf. Now as for the integration by partial fraction, try solving this equation for A, B and C by setting x to certain values(in order to eliminate only A, B or C):

$$\frac{x^{2}+2x-1}{2x^{3}+3x^{2}-2x}=\frac{A}{x}+\frac{B}{x+2}+\frac{C}{2x-1}$$

Then you'll be able to integrate.

 

[oyala]

hey thank you so much.
you explain it better than what I thought


great work !

 

[grindfreak]

Anytime man, I appreciate the feedback.