`intx/((x^2-a^2)(x^2-b^2))dx`

Answer

To solve the integral

\[ \int \frac{x}{(x^2 - a^2)(x^2 - b^2)} \, dx, \]

we can use partial fraction decomposition. Let's break down the solution step by step.

### Step 1: Rewrite the integrand using partial fractions

We can express the integrand as:

\[ \frac{x}{(x^2 - a^2)(x^2 - b^2)} = \frac{A}{x^2 - a^2} + \frac{B}{x^2 - b^2}, \]

where \( A \) and \( B \) are constants to be determined.