Question

How do you integrate `[(x + 4)/(x^2 + 8 x +17)] dx`?

Answer 1

Use substitution:

`(x+4)/(x^2+8x+17) = (x+4)/(x^2+8x+16+1) = (x+4)/((x+4)^2+1)`

Now with `u=x+4` this becomes `u/(u^2+1)` whose integral (by another substitution) is

`1/2 ln (u^2+1) +C`

Finish by going back to the variable `x`.