Specialist Mathematics · integration techniques · explainer

Parts is the product rule backwards

The product rule says (uv)′ = u′v + uv′. Rearrange, then integrate both sides — that identity is integration by parts. Check by differentiating the answer.

y = x eˣ tangent = (uv)′ u′v = eˣ

Drag x on the curve · the two cards always add to the tangent slope

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Product rule → parts