Evaluate an indefinite integral of a polynomial expression raised to a high power multiplied by another polynomial using u-substitution.

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Integrating a Polynomial with a High Power Using Substitution

Antiderivatives warmup

Find \( \int (2x^3 + x)(x^4 + x^2 + 1)^{49} \, dx \).

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What you need first

Derivatives of polynomials
The power rule for integration
The method of integration by substitution

What this problem tests

Tests the ability to identify an inner function whose derivative is present as a factor in the integrand, and to correctly execute the substitution and integration steps.

This is a standard introductory calculus problem designed to practice recognizing when and how to apply u-substitution.

Integrating a Polynomial with a High Power Using Substitution

What you need first

What this problem tests

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