Find indefinite integral. ∫x^2 ln2 x d x

Name: Problem 14, Chapter 7: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-05-16T09:00:48-08:00
Duration: 3 min 39 s
Channel: Naresh Bagrecha
Description: Find indefinite integral. ∫x^2 ln2 x d x

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Key Concepts

Indefinite Integration

Indefinite integration involves finding a function whose derivative is the given integrand, often referred to as the antiderivative. It is the reverse process of differentiation and includes an arbitrary constant because differentiation of a constant yields zero.

Integration by Parts

Integration by parts is a method used to integrate products of functions. It is based on the product rule for differentiation and transforms the integral of a product into an expression involving the integral of a related product, making it particularly useful when one of the functions simplifies upon differentiation.

Properties of Logarithms

Properties of logarithms, such as the rule that the logarithm of a product can be expressed as the sum of the logarithms, are useful in integration. These properties allow the manipulation of logarithmic expressions to simplify the integrand and facilitate the integration process.

Polynomial Integration

Polynomial integration refers to the process of integrating polynomial functions term by term. Since polynomials have straightforward power functions, each term can be integrated using the basic power rule, which is a fundamental technique in calculus.

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