Find the indefinite integral. ∫((1)/(x^2)-(1)/(√(x^2))+(1)/(√(x))) d x

Name: Problem 46, Chapter 11: Applied Mathematics: For the Managerial, Life, and Social Sciences
Uploaded: 2021-05-09T08:43:44-08:00
Duration: 2 min 24 s
Channel: Nishant Tyagi
Description: Find the indefinite integral. ∫((1)/(x^2)-(1)/(√(x^2))+(1)/(√(x))) d x

step 1 The given function is integral of 1 divided by x square minus 1 divide by cube root of x square

Find the indefinite integral....

Key Concepts

Indefinite Integration

Indefinite integration refers to the process of finding the antiderivative of a function. This involves determining a family of functions whose derivative yields the original function. Since there is an arbitrary constant involved in differentiation, the result of an indefinite integral includes an added constant, typically represented as C.

Power Rule for Integration

The power rule for integration is a basic technique for finding the antiderivative of functions in the form x^n, where n is any real number other than -1. It states that the antiderivative of x^n is x^(n+1) divided by (n+1), plus an arbitrary constant. This rule simplifies the process of integrating power functions and is widely applied in calculus.

Exponent Rules

Exponent rules are essential for rewriting functions involving roots and powers into a form that is easier to integrate. For example, expressing radicals as fractional exponents allows one to apply the power rule for integration directly. Understanding and correctly applying these exponent rules ensure accurate transformation and subsequent integration of the function.

Constant of Integration

The constant of integration is an arbitrary constant added to the antiderivative when computing an indefinite integral. It accounts for the fact that the differentiation process eliminates any constant term, meaning that the antiderivative is not unique but rather represents a family of functions. Including this constant is crucial for expressing the complete set of solutions.

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