Vault Of Euclid

Integrating a Squared Rational Function by Expansion

Antiderivatives warmup

Find \( \int \left(\frac{x^2+1}{x}\right)^2 \, dx \).

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What you need first

Expanding binomials
Laws of exponents
The power rule for indefinite integrals

What this problem tests

Tests the student's ability to recognize when to simplify an integrand algebraically rather than attempting a more complex integration technique.

This is a standard introductory calculus problem demonstrating that algebraic simplification is often the best first step before integrating.

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