Word Count : 335

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a) Consider the integral [ \int_0^{\infty} \frac{x^2 + 2}{(x^2 + 1)(x^2 + 4)} , dx. ] Use partial fraction decomposition: [ \frac{x^2 + 2}{(x^2 + 1)(x^2 + 4)} = \frac{A}{x^2 + 1} + \frac{B}{x^2 + 4}. ] Multiply both sides by ((x^2 + 1)(x^2 + 4)): [ x^2 + 2 = A(x^2 + 4) + ____ _______ __________ _____ ____ __________ __________ ______ _____.
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