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1. Find the partial fraction decomposition for the rational function x2 - x+5 x3+x 2. Use the partial fraction decomposition of the function to evaluate

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1. Find the partial fraction decomposition for the rational function x2 - x+5 x3+x 2. Use the partial fraction decomposition of the function to evaluate the integral x +5 x(x - 1)2 dx Solving using a formula is not acceptable. 4. First complete the square, make the appropriate substitutions, and then evaluate the integral: 1 dx x - 2x +5

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