Vault Of Euclid

Integrating a Polynomial by Expansion

Antiderivatives warmup

Find \( \int (2-x^3)^2 x \, dx \).

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What you need first

Basic algebraic expansion
The power rule for integration
Understanding when substitution is applicable

What this problem tests

Tests the student's ability to recognize when substitution fails and to fall back on algebraic expansion to evaluate an integral.

This is a standard introductory calculus problem demonstrating that algebraic manipulation is often necessary before integrating.

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