Integration techniques · manipulative

Partial fractions as the same graph

The rational is the target. Scrub A and B until the teal sum A/(x−p)+B/(x−q) locks onto it — then the integral splits into two logarithms.

rational A/(x−p)+B/(x−q)

Dashed lines are the poles — curves break there. Soft-snap when A, B are close.

Coefficients

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Working