Evaluate the integral. \[ \int_{0}^{3} \frac{x^{2}+x+1}{(x+1)^{2}(x+2)} d x \]
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We need to express \(\frac{x^2 + x + 1}{(x+1)^2(x+2)}\) in the form: \[ \frac{x^2 + x + 1}{(x+1)^2(x+2)} = \frac{A}{x+1} + \frac{B}{(x+1)^2} + \frac{C}{x+2} \] Show more…
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