Vault Of Euclid

Reduction Formula for x^n sin(ax)

Techniques of integration core

Find a reduction formula for \( \int x^n \sin ax \, dx \) for \( n \ge 1 \).

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What you need first

Integration by parts
Derivatives of polynomials
Antiderivatives of trigonometric functions

What this problem tests

Tests the ability to correctly choose parts for integration by parts and apply the formula to derive a general reduction rule.

This is a standard exercise in a Calculus II course when learning integration by parts and reduction formulas.

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Integral of a Rational Function using Partial Fractions core
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Integral of x^2 arctan(x) core
Reduction Formula for a Rational Function core
Area Under the Curve of ln(x)/x warmup

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