step 1 Hi there's a question. In this I have d x by e a aides to the power x I have to integrate it by

∫(d x)/(e^x) | Numerade

Name: Problem 49, Chapter 5: Calculus Early Transcendentals
Uploaded: 2023-02-23T00:48:39-08:00
Duration: 1 min 11 s
Channel: Khushbu Rani
Description: ∫(d x)/(e^x)

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Key Concepts

Indefinite Integration

Indefinite integration involves finding the antiderivative of a function, meaning the process of determining a function whose derivative equals the given integrand. This operation yields a family of functions that differ by a constant, and it serves as the inverse process to differentiation.

Exponential Functions

Exponential functions, characterized by the constant e raised to a variable power, have unique properties in calculus due to their invariant behavior under differentiation and integration. They are widely used in various applications, including modeling growth and decay processes.

Integration of Exponential Functions

When integrating exponential functions, standard formulas are often applied, such as the antiderivative of e^(kx) being equal to (1/k)e^(kx) plus a constant of integration, provided k is a nonzero constant. This technique simplifies the integration process for functions involving exponential expressions.

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