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[DTube] Reduction Formula for Integral of ∫ln^n(x)dx

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Published: 26 Jan 2019 › Updated: 26 Jan 2019[DTube] Reduction Formula for Integral of ∫ln^n(x)dx

[DTube] Reduction Formula for Integral of ∫ln^n(x)dx

In this video, we work through the derivation of the reduction formula for the integral of lnn(x) or [ln(x)]n.

Like with lower powers of ln(x), such as ln2(x), we adopt the same approach of integration by parts, letting u = lnn(x) and dv = dx.

We then use the our derived formula to find the indefinite integral of ln3(x).

Integration: Reduction Formulas

  1. Reduction Formula for Integral of ∫sinn(x)dx
  2. Reduction Formula for Integral of ∫cosn(x)dx
  3. Reduction Formula for Integral of ∫tann(x)dx
  4. Reduction Formula for Integral of ∫lnn(x)dx

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