u-substitution with manipulation

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What is u-substitution in integration?

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U-substitution is a method used to simplify integrals by substituting a part of the integrand with a new variable, u, making the integral easier to solve.

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What is the purpose of choosing u in u-substitution?

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Choosing u simplifies the integral, often transforming it into a basic form that can be easily integrated.

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What is the chain rule in calculus?

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The chain rule is a formula for computing the derivative of the composition of two or more functions.

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How do you apply the chain rule in u-substitution?

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When using u-substitution, the chain rule helps to relate the derivative of u back to the original variable, allowing for proper integration.

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