How to Integrate Rational Functions with Unfactorable Denominators

[Hamid1]

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:)

 

[virus]

Are you interested in the answer or the method?
If you need just the answer then you can use "www.integrals.wolfram.com "

 

[Hamid1]

Yes,I want the method.

 

[virus]

rewrite the numerator as (2x+4-4)/2.Try splitting the integral into two functions now.

 

[Hootenanny]

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?

 

[Hamid1]

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.

 

[virus]

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.

 

[Hamid1]

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?

 

[Hootenanny]

Thank you.the first part is easy to solve but how can I solve the second part?

Use partial fractions.

 

[HallsofIvy]

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.

 

[Hamid1]

Use partial fractions.

Can you tell me how?Because I don't know english(partial fractions) very well.

 

[Hootenanny]

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?

 

[HallsofIvy]

No, the whole point of this problem is that you cannot factor the denominator. Complete the square instead.

 

[Hootenanny]

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*