-1 tanx 4. 1+x?

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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Use basic substitution to evaluate the following integrals.

The expression shown is an integral that needs to be evaluated:

\[
\int \frac{e^{\tan^{-1}x}}{1 + x^2} \, dx
\]

This integral involves the exponential function raised to the inverse tangent function, divided by a sum of 1 and the square of \(x\). The denominator, \(1 + x^2\), suggests that a substitution involving the derivative of \(\tan^{-1}x\) might simplify the integration process.

This type of integral is common in calculus courses, often requiring substitution or integration techniques to solve.
Transcribed Image Text:The expression shown is an integral that needs to be evaluated: \[ \int \frac{e^{\tan^{-1}x}}{1 + x^2} \, dx \] This integral involves the exponential function raised to the inverse tangent function, divided by a sum of 1 and the square of \(x\). The denominator, \(1 + x^2\), suggests that a substitution involving the derivative of \(\tan^{-1}x\) might simplify the integration process. This type of integral is common in calculus courses, often requiring substitution or integration techniques to solve.
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