# Can anyone integrate this?

1. Dec 6, 2008

### 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:)

2. Dec 6, 2008

### virus

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

3. Dec 6, 2008

### Hamid1

Yes,I want the method.

4. Dec 6, 2008

### virus

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

5. Dec 6, 2008

### Hootenanny

Staff Emeritus
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. Dec 6, 2008

### Hamid1

can you explain more?
I have solved about 100 integrals but I can't do these two.I don't know the method.
thank you.

7. Dec 6, 2008

### 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.

8. Dec 6, 2008

### Hamid1

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

9. Dec 6, 2008

### Hootenanny

Staff Emeritus
Use partial fractions.

10. Dec 6, 2008

### HallsofIvy

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. Dec 6, 2008

### Hamid1

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

12. Dec 6, 2008

### Hootenanny

Staff Emeritus
Can you factorise the denominator and then split the fraction into two different fractions?

13. Dec 6, 2008

### HallsofIvy

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

14. Dec 6, 2008

### Hootenanny

Staff Emeritus
Whoops! I thought the denominator was (x2-4x-5).