# How do you integrate #(x)/(x+10) dx#?

##### 1 Answer

You could use two ways - pure algebra or partial fractions - either of which give you

#### Explanation:

**Algebraic Approach**

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:

Since

**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

Therefore

I would not suggest the partial fractions method unless you were required to use it.