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
The solution and a full step-by-step explanation are here. Sign in to read them.