Integrating Partial Fractions: Solving a Challenging Integral

In summary, the conversation includes a student seeking help with a math problem involving integration with partial fractions. After struggling for 3 hours, the student receives a hint to try a substitution method and successfully solves the problem. The final solution is 4/3.
  • #1
Matty R
83
0
Hello :smile:

I've been stuck on this question for almost 3 hours now, and I still have no idea what to do. We haven't done a question like this in class, although we have done integration with partial fractions.

Homework Statement



Evaluate:

http://img43.imageshack.us/img43/4110/34519231.jpg


Homework Equations





The Attempt at a Solution


http://img230.imageshack.us/img230/7321/21305382.jpg

http://img230.imageshack.us/img230/4774/89099153.jpg

If I make A and B equal 0, I get C = 6. Then I just end up with the same integral as I started with.

I'd really appreciate any help with this. :smile:

Thank you
 
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  • #2
No need for partial fractions. Try letting u = 2x - 1.
 
  • #3
I was convinced it had something to do with partial fractions. :redface:

I've just done the u substitution thingy and 4/3, which is the correct answer.

Thank you very much for your help. :smile:
 

1. What is partial fractions integration?

Partial fractions integration is a method used to integrate rational functions, which are functions that can be written as the quotient of two polynomials. It involves breaking down a complicated rational function into smaller, simpler fractions that can be integrated using basic integration techniques.

2. When is partial fractions integration used?

Partial fractions integration is typically used when integrating improper rational functions, where the degree of the numerator is greater than or equal to the degree of the denominator. It is also used when integrating rational functions with repeated factors in the denominator.

3. What is the process for integrating partial fractions?

The general process for integrating partial fractions involves breaking down the rational function into simpler fractions, finding the coefficients for each fraction, and then integrating each fraction using basic integration techniques. The final step is to combine the individual integrals to get the overall integral.

4. Are there any special cases to consider when integrating partial fractions?

Yes, there are a few special cases to consider when integrating partial fractions. These include when the rational function has complex roots, when the denominator has repeated factors, and when the degree of the numerator is greater than or equal to the degree of the denominator. In these cases, different methods may need to be used for finding the coefficients and integrating the fractions.

5. Can partial fractions integration be used for all rational functions?

No, not all rational functions can be integrated using partial fractions. Some functions may require more advanced integration techniques, such as trigonometric substitutions or integration by parts. It is important to check the conditions for using partial fractions integration before attempting to integrate a rational function.

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