U-substitution

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What is U-substitution in integration?

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U-substitution is a method used to simplify the process of integration by substituting a part of the integrand with a new variable, usually denoted as 'u', to make the integral easier to solve.

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When should you use U-substitution?

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Use U-substitution when the integrand is a composite function or when a function and its derivative appear in the integral.

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What is the first step in U-substitution?

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Identify a part of the integrand to substitute with 'u', typically a function whose derivative is also present in the integrand.

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How do you express dx in terms of du during U-substitution?

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After substituting u, differentiate u with respect to x to find du, and then express dx in terms of du.

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What is the formula for U-substitution?

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What is the importance of the constant C in integration?

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The constant C represents the family of antiderivatives, as indefinite integrals can differ by a constant.