# What is the net area between #f(x)=(x-x^2)/ln(x^2)# in #x in[1,2] # and the x-axis?

##### 1 Answer

The integral of this function cannot be evaluated with elementary functions. If you approximate it on a calculator, you'll get

#### Explanation:

If you type "integrate (x-x^2)/ln(x^2)" into Wolfram Alpha you'll see that "nonelementary (special) functions " become involved. This not helpful for most students. Therefore, you should approximate the integral either with technology (or maybe Simpson's Rule with technology) to get **Note:** there is a removable singularity (hole in the graph) at

The "net (signed) area" is about

The graph can be used to confirm this visually.

graph{(x-x^2)/ln(x^2) [-10, 10, -5, 5]}