How do you integrate #(x)/(x+10) dx#?
You could use two ways - pure algebra or partial fractions - either of which give you
First, realize that we can rewrite the integral as:
Now we can split it up into two fractions, like so:
Using the sum rule for integrals, this further simplifies to:
Evaluating these is pretty straightforward now:
Partial Fractions Approach
Alternatively, if we want some practice with partial fractions or the teacher is forcing us to use this method, we can do it a little differently.
Since our original fraction
Setting it up, we have:
Multiplying through by
If we let
Now we have:
We can let
I would not suggest the partial fractions method unless you were required to use it.