Integration by Parts

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Hook

Reversing the product rule

U-substitution reverses the chain rule. Integration by parts reverses the PRODUCT rule. It carves an integral into two pieces and trades a hard one for an easier one. The formula: ∫u dv = uv − ∫v du. Pick u wisely and the new integral is simpler than the one you started with.

Integration by parts = reverse product rule. ∫u dv = uv − ∫v du.

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