# How do you integrate #int (x+4)/(x^2+4x-5) dx# using partial fractions?

##### 1 Answer

#### Explanation:

1) First step is to factorize the denominator of your fraction completely:

In case you don't know how to do this:

- solve the quadratic equation

- find the solutions

- your factorization is

2) Now that you have the factorization, you need to decompose your fraction into partial fractions.

This means that you are searching for

... multiply both sides of the equation with

To solve this equation, you need to compare the

The solution of this linear equation system is

This means that you have succeded in the partial fraction decomposition:

3) The only thing left to do is solving the integral. :-)