# Integration (by substitution?)

1. May 25, 2005

### Guero

how can i integrate:
x^2+7x+10 dx
x+2

i assume it's by substitution, but i can't work it out.

sorry for the formatting, btw

2. May 25, 2005

### whozum

Factor the top, it cancels.

3. May 25, 2005

### minase

(x+5)(X+2) =x+5
(x+2)
I don't know nothing about integrate. But I think you have to factor the trinomial then divide.

4. May 25, 2005

### whozum

Note the singularity at x = -2, it cant be integrated in a region containing this point.

5. May 25, 2005

### dextercioby

Not really.It can't be defined at x=-2,which means that automatically that point is excluded from the integration domain.

Daniel.

6. May 25, 2005

### Guero

thanks. should've seen it.

7. May 25, 2005

### whozum

Does the integral

$$\int_{-3}^1 \frac{x^2+7x+10}{x+2} \ dx$$ exist, dex? As its written?

8. May 25, 2005

### dextercioby

I don't know.U'll have to break it into 2 and evaluate each limit.(I wasn't talking about a definite integral,so your (counter)example is useless).

Daniel.

9. May 25, 2005

### whozum

Its the same thing.

10. May 25, 2005

### HallsofIvy

Staff Emeritus
However, the integral is a "smoothing" operation. The integral of a function with removable discontinuity exists and is exactly the same as the integral of the function with the discontinuity removed.

11. May 25, 2005

### what

whozum do you agree that x^2 is integratable, what about $$\frac{(x^2)(x+1)}{x+1}$$?

12. May 25, 2005

### whozum

Theyre both integrable, just the latter isnt continuous.