3. For what value or values of \( a \) does \[ \int_{1}^{\infty} \left( \frac{ax}{x^2+1} - \frac{1}{2x} \right) dx \] converge? Evaluate the corresponding integral(s). (10 %)
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3. For what value or values of \( a \) does \[ \int_{1}^{\infty} \left( \frac{ax}{x^2+1} - \frac{1}{2x} \right) dx \] converge? Evaluate the corresponding integral(s). (10 %)