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10 cards from this deck
To simplify a rational function for easier integration.
Factor the denominator into linear or quadratic terms.
As a sum of simpler fractions based on the factors.
Solve for the constants in the partial fractions.
Decompose into simpler fractions, then integrate each.
Use (Ax+B)/(x2+a)(Ax + B) / (x^2 + a)(Ax+B)/(x2+a) for quadratic factors.
Result is 18ln∣x−4∣−18ln∣x+4∣+C\frac{1}{8}\ln|x-4| - \frac{1}{8}\ln|x+4| + C81ln∣x−4∣−81ln∣x+4∣+C.
Set up an equation and solve for unknown constants.
To simplify integration of rational functions.
They are simplified to make integration manageable.
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