When and where to apply u substitution

[EdTheHead]

I ran into this problem here

[math]\int {1}{x^2 + 7x + 10}dx[/math]

and the only way I can think of to solve this kinda thing is to do a substitution and get [math]u^-1[/math] but in this case I have no idea how to turn the substitute in the du. Is this a trig substitution problem?

[Cap'n Refsmmat]

Did you mean this?

 

[math]\int \frac{1}{x^2 + 7x +10}\, dx[/math]

 

If so, you can probably do this:

 

[math]\int \frac{1}{(x + 2)(x+5)} \, dx[/math]

 

and use partial fraction decomposition to solve it.

[EdTheHead]

Sorry yeah thats what I meant. Ah right I didn't think of partial fractions thanks.