c) Evaluate 

To evaluate the integral \(\int e^x \frac{x^2 - x + 1}{(1 + x^2)^{3/2}} \, dx\), we can use the method of integration by parts and substitution. Here's the step-by-step process:

1. **Substitution**: Let \(u = 1 + x^2\). Then \(du = 2x \, dx\) or \(dx = \frac{du}{2x}\).
   
   Note that \(x^2 = u - 1\) and hence \(x = \sqrt{u - 1}\).

2. **Simplify the Integral**: Rewrite the integral in terms of \(u\).

   Given the integrand \(\frac{x^2 - x + 1}{(1 + x^2)^{3/2}}\), we first express it in terms of \(u\):
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