# Help with 2 integrals

1. Dec 2, 2009

### zombieguy

1. The problem statement, all variables and given/known data

How do I do these 2?

a) x/(x^2+x-6)

b) 4/(x^2+4x+4)

2. Relevant equations

3. The attempt at a solution

a) Tried quotient rule it gave me -x^2 - 6/(x^2+x+6)^2, I don't think it's right

b) Tried substitution (because theres another similar question between these two on the paper and that was the way to go for it) Don't think my answers worth mentioning

2. Dec 2, 2009

### Dick

There's no 'quotient rule' for integrals! Try partial fractions.

3. Dec 2, 2009

### darkmagic

Factor first the denominator then use the partial fractions.

4. Dec 2, 2009

### zombieguy

Ok, Thanks

I've now got:

a) 3/5ln(x+3)+2/5ln(x-2)

b) 2/(x+2)ln(x+2)^2

Is that right?

5. Dec 2, 2009

### Staff: Mentor

Part b is not correct. After factoring you have
$$\int \frac{4}{(x + 2)^2}~dx$$

You can do this with an ordinary substitution. Your answer should NOT have a log in it!

6. Dec 2, 2009

### Dick

If you mean (3/5)ln(x+3)+(2/5)ln(x-2), (use more parentheses!) then the first one looks ok. I don't like the looks of the second one. If you had shown your work, I might have been able to tell you where you went wrong.

Last edited: Dec 2, 2009
7. Dec 3, 2009

### zombieguy

OK, I've tried b) again but this time by using:

u.v-(integral of)(v.du/dx)

u=4
du/dx=0 (That gets rid of the integral part)

v=-(x+2)^-1
dv/dx= (x+2)^-2

so: 4.-(x+2)^-1

It would be nice if you could show me how to do it your way (using substitution) aswel

8. Dec 3, 2009

### Dick

Let u=(x+2). du=dx. Then 4/(x+2)^2 dx=4/u^2 du=4*u^(-2) du. Use the power law integral u^n=u^(n+1)/(n+1).

9. Dec 3, 2009

### zombieguy

Thank you all for your help