Word Count : 291

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We are asked to evaluate: [ \int \frac{1}{(x-2)(x^2+4)} , dx ] First, decompose the integrand using partial fractions: [ \frac{1}{(x-2)(x^2+4)} = \frac{A}{x-2} + \frac{Bx + C}{x^2 + 4} ] Multiply through by ((x-2)(x^2+4)): [ 1 = A(x^2 + 4) + (Bx + C)(x-2) ] Expand the right-hand side: [ 1 = A x^2 + 4A + Bx^2 - 2Bx + Cx - 2C ] Combine like terms: [ 1 = (A + __________ ______ ______ _________ _____ _________.
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