How to Integrate Rational Functions with Unfactorable Denominators

  • Thread starter Hamid1
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In summary, you can try integrating the numerator first, then factoring the denominator. Partial fractions can help you with the second part.
  • #1
Hamid1
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Hi all.
can anyone integrate xdx/x^2+4x+5
and this one : xdx/sqrt(x^2+4x+13)

thank you and excuse me for english:)
 
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  • #2
Are you interested in the answer or the method?
If you need just the answer then you can use "www.integrals.wolfram.com "
 
  • #3
Yes,I want the method.
 
  • #4
rewrite the numerator as (2x+4-4)/2.Try splitting the integral into two functions now.
 
  • #5
Hamid1 said:
Yes,I want the method.
That's not the way it works here. We will help you with your homework, but we will not do it for you. You have to put some effort in.

What have you tried thus far?
 
  • #6
rewrite the numerator as (2x+4-4)/2.Try splitting the integral into two functions now.
can you explain more?
That's not the way it works here. We will help you with your homework, but we will not do it for you. You have to put some effort in.
I have solved about 100 integrals but I can't do these two.I don't know the method.
thank you.
 
  • #7
rewrite as integral of 1/2*( 2x+4/x^2+4x+5) -2*integral of (1/x^2+4x+5) . Now try to solve both of these integrals seperately.
 
  • #8
virus said:
rewrite as integral of 1/2*( 2x+4/x^2+4x+5) -2*integral of (1/x^2+4x+5) . Now try to solve both of these integrals seperately.
Thank you.the first part is easy to solve but how can I solve the second part?
 
  • #9
Hamid1 said:
Thank you.the first part is easy to solve but how can I solve the second part?
Use partial fractions.
 
  • #10
Hamid1 said:
Hi all.
can anyone integrate xdx/x^2+4x+5
and this one : xdx/sqrt(x^2+4x+13)

thank you and excuse me for english:)
Since you have "xdx" in the numerator- which should remind you of the derivative of x2, you should immediately think about getting the denominator in the form "x2- a" so you can substitute. In other words, start by completing the square in the denominator.
 
  • #11
Hootenanny said:
Use partial fractions.
Can you tell me how?Because I don't know english(partial fractions) very well.
 
  • #12
Hamid1 said:
Can you tell me how?Because I don't know english(partial fractions) very well.
Can you factorise the denominator and then split the fraction into two different fractions?
 
  • #13
No, the whole point of this problem is that you cannot factor the denominator. Complete the square instead.
 
  • #14
HallsofIvy said:
No, the whole point of this problem is that you cannot factor the denominator. Complete the square instead.
Whoops! I thought the denominator was (x2-4x-5).

*Slinks back off to physics*
 

FAQ: How to Integrate Rational Functions with Unfactorable Denominators

Can anyone integrate this without prior knowledge or training?

No, integration requires a certain level of understanding and knowledge in mathematics and problem solving. It is not something that can be done without any prior experience or training.

Is integration a difficult concept to grasp?

It can be challenging for some people to understand, but with practice and patience, it can become easier to grasp. It is important to have a strong foundation in basic mathematics before attempting to learn integration.

What are the benefits of being able to integrate?

Integration is a fundamental tool in many areas of science, engineering, and economics. It allows for the calculation of areas, volumes, and averages, which are essential in analyzing and solving real-life problems.

Can I use a calculator to perform integration?

Yes, there are many online and handheld calculators that have integration capabilities. However, it is important to understand the concepts and steps involved in integration in order to use a calculator effectively.

How can I improve my integration skills?

Practice, practice, practice! Integration, like any other skill, requires practice to become proficient. It is also helpful to seek out resources such as textbooks, online tutorials, and practice problems to further develop your skills.

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