Question

How do you evaluate the integral `int (2x^2+x-5)/((x-3)(x+2))`?

Answer 1

`int (2x^2+x-5)/(x^2-x-6)*dx=2x+2ln(x-3)-ln(x+2)+C`

Explanation:

`int (2x^2+x-5)/(x^2-x-6)*dx`

=`int 2dx`+`int (x+7)/(x^2-x-6)*dx`

=`2x+int (x+7)/((x-3)*(x+2))*dx`

=`2x+int (2x+4)/((x-3)(x+2))*dx`-`int (x-3)/((x-3)(x+2))*dx`

=`2x+int (2dx)/(x-3)`-`int (dx)/(x+2)`

=`2x+2ln(x-3)-ln(x+2)+C`