Vault Of Euclid

Reduction Formula for a Rational Function

Techniques of integration core

Prove the reduction formula \( \int \frac{x^2 \, dx}{(a^2+x^2)^n} = \frac{-x}{(2n-2)(a^2+x^2)^{n-1}} + \frac{1}{2n-2} \int \frac{dx}{(a^2+x^2)^{n-1}} \).
integration-by-partsreduction-formularational-functionsubstitutioncalculus-iiindefinite-integralalgebraic-manipulationpower-rule

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What this problem tests

Tests the ability to strategically choose parts for integration by parts and correctly apply substitution to find the antiderivative of the chosen dv.

This type of reduction formula is commonly encountered in Calculus II courses when dealing with trigonometric substitutions or partial fractions.

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