Find indefinite integral. ∫x √(x-5) d x

Name: Problem 11, Chapter 7: Applied Calculus for the MLSS A Brief Approach
Uploaded: 2021-05-16T08:45:37-08:00
Duration: 3 min 34 s
Channel: Naresh Bagrecha
Description: Find indefinite integral. ∫x √(x-5) d x

Key Concepts

Algebraic Manipulation

Algebraic manipulation refers to the process of rewriting and simplifying expressions within an integral. This includes techniques such as expanding or rewriting functions in terms of a new variable, which is often necessary to apply standard integration rules effectively.

Indefinite Integration

Indefinite integration involves finding a function that differentiates to the given integrand, representing a family of functions that differ by an arbitrary constant. This concept is fundamental in calculus for recovering original functions from their rates of change.

Substitution Method

The substitution method, or u-substitution, is a technique used to simplify complex integrals by changing variables. This method is particularly effective when the integrand contains a composite function, allowing the integral to be rewritten in a more manageable form.

Integration of Radical Expressions

The integration of radical expressions involves handling integrals that contain roots, such as square roots. This typically requires rewriting the radical in exponent form or using substitution techniques to transform the integrand into a form that can be integrated using standard formulas.

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