Unformatted text preview: high degree polynomials in the denominator for which one has to ﬁnd the antiderivative function. So we shall explain how to ﬁnd the antiderivative of a rational function only when the denominator is a quadratic polynomial ax 2 + bx + c . We should mention a special type of rational function that we already know how to integrate: If the denominator has the form ( ax + b ) n , the substitution u = ax + b will always work. The denominator becomes u n , and each x in the numerator is replaced by ( ub ) /a , and dx = du/a . While it may be tedious to complete the integration if the numerator has high degree, it is merely a matter of algebra....
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 Spring '07
 JonathanRogawski
 Math, Calculus, Antiderivatives, Derivative, Fraction, Rational function, dx

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