Evaluate the following integrals

a) 

b) 

a) 

\[ \int_{0}^{\infty}\frac{x^2 + 2}{(x^2 +1)(x^2 + 4)}dx \]

To solve this integral, we can use partial fraction decomposition. The integrand can be rewritten as:

\[ \frac{x^2 + 2}{(x^2 +1)(x^2 + 4)} = \frac{A}{x^2 + 1} + \frac{Bx + C}{x^2 + 4} \]

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