Evaluate `int_1^(3/2) abs(xsin(pix))dx`

Explanation

To evaluate the integral \( \int_1^{\frac{3}{2}} |x \sin(\pi x)| \, dx \), we need to analyze the function \( f(x) = x \sin(\pi x) \) over the interval from 1 to \( \frac{3}{2} \).

### Step 1: Determine the Sign of \( f(x) \)

First, we need to find the points where \( f(x) \) changes sign in the interval \( [1, \frac{3}{2}] \).

- At \( x = 1 \):
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