Question is down below, thanks :) The given mathematical expression is:\[ \int x \sec^2(x^2) \, dx \]This represents the integral of the function $ x \sec^2(x^2) $ with respect to $ x $. ### Explanation:- $ \int $ : This is the integral sign, indicating the operation of integration.- $ x $ : This is the variable in the integrand.- $ \sec^2(x^2) $ : The function being integrated, where $ \sec $ stands for the secant function, and $ \sec^2 $ indicates the secant function squared. The argument of the secant function is $ x^2 $.- $ dx $ : This indicates the variable of integration.Integration is a fundamental concept in calculus and involves finding the antiderivative of a given function. Integrals are used to calculate areas under curves, among other applications. This particular integral involves trigonometric functions, adding complexity to the integration process.

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Calculus

|r sec" (z*) dz

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question is down below, thanks :)

The given mathematical expression is:

\[ \int x \sec^2(x^2) \, dx \]

This represents the integral of the function $ x \sec^2(x^2) $ with respect to $ x $.

### Explanation:
- $ \int $ : This is the integral sign, indicating the operation of integration.
- $ x $ : This is the variable in the integrand.
- $ \sec^2(x^2) $ : The function being integrated, where $ \sec $ stands for the secant function, and $ \sec^2 $ indicates the secant function squared. The argument of the secant function is $ x^2 $.
- $ dx $ : This indicates the variable of integration.

Integration is a fundamental concept in calculus and involves finding the antiderivative of a given function. Integrals are used to calculate areas under curves, among other applications. This particular integral involves trigonometric functions, adding complexity to the integration process.

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