Integral involving partial fractions and roots

In summary, the person is thanking the forum for their help and appreciating the way people are providing ideas instead of just giving answers. They also mention having trouble with partial fractions and provide an example of their issue. Another person suggests canceling out the common factor of u in the fraction to simplify the integral.
  • #1
prace
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PS. Just wanted to say thanks for all the help so far. This is a really great forum and I am receiving tons of help. I like how people here are not just blurting the answers, but are actually feeding me ideas so that I may work them out. Everyone here is really helping me learn this stuff! Thanks again. :smile:
 
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  • #2
Well, you forgot to do partial fractions! (e.g. you didn't factor the denominator...)
 
  • #3
:-p haha... I know the demoninator is not factored there. I just left the equation like that so it was complete for the posting. I know I have to factor it and do the whole partial fractions bit, but this is where my problem lies.

For example, what I have on paper is that I took the 272 out of the integral, which left u/(u(u+4)) inside the integral.

But then the partial fractions do not come out right for me.
 
  • #4
There is a common factor of u in both the numerator and denominator of that fraction, cancel it out and then it should be a very simple integral.
 

FAQ: Integral involving partial fractions and roots

What is the purpose of using partial fractions in integrals?

The purpose of using partial fractions in integrals is to simplify complex fractions into smaller, more manageable fractions that can be easily integrated. This is especially useful when dealing with integrals containing rational functions.

How do you determine the partial fraction decomposition of a rational function?

The partial fraction decomposition of a rational function can be determined by first factoring the denominator into linear and irreducible quadratic factors. Then, the coefficients of the partial fractions can be found by using the method of undetermined coefficients or by setting up a system of equations and solving for the unknown coefficients.

Can you use partial fractions to integrate functions with repeated roots?

Yes, partial fractions can be used to integrate functions with repeated roots. In this case, the partial fraction decomposition will include a term with a higher power of the repeated root in the denominator, which can be integrated using techniques such as substitution or integration by parts.

What is the purpose of including roots in a partial fraction decomposition?

Including roots in a partial fraction decomposition is necessary to handle cases where the denominator of the rational function has irreducible quadratic factors. These roots will correspond to terms in the partial fraction decomposition that cannot be further simplified into linear factors.

Are there any special cases to consider when using partial fractions in integrals?

Yes, there are a few special cases to consider when using partial fractions in integrals. These include integrals with complex roots, integrals with repeated roots, and integrals with irreducible quadratic factors in the denominator. In these cases, additional steps may be required to properly decompose the rational function and integrate it.

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