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On Abel’s Theorem
Choose only one of the following two exercises.
Exercise A. Express the following two elementary indefinite integrals in terms of only rational functions, square roots and logarithms
1.
∫ x3dx x2 −3x+ 2, 2.
∫ dx
√x2 −3x+ 4.
Hint. For the second integral use the substitution t = (y−2)/x, where y is the square root y = √
x2−3x + 4.
Exercise B (if you don’t like calculus). Write a short essay (around one page–in English!) about the life of Niels Henrik Abel.
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