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MathCalculus

Partial Fractions: Integrate 1/[(x − 3)(x − 2)]

Decompose the rational integrand in OpenStax Calculus Volume 2 exercise 196, integrate the terms, and keep the excluded poles explicit.

Question

OpenStax Calculus Volume 2, §3.4, exercise 196: Use the method of partial fractions to evaluate

∫dx(x−3)(x−2).\int\frac{dx}{(x-3)(x-2)}.

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Evidence boundary

No initial condition is given. The expression is valid on each interval of the original domain, (−∞,2)(-\infty,2), (2,3)(2,3), and (3,∞)(3,\infty); the arbitrary constants on these intervals need not be equal.