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1. Sx arctan x? dx =x² arctan(x²) – In(1 + x*) + C

1. Sx arctan x? dx =x² arctan(x²) – In(1 + x*) + C

Calculus: Early Transcendentals
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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1. \( \int x \, \arctan{x^2} \, dx \) --- Explanation: This is an integral calculus problem requiring the integration of the product of \(x\) and \(\arctan(x^2)\). Possible methods for solving this could include integration by parts or trigonometric substitution.
Transcribed Image Text:1. \( \int x \, \arctan{x^2} \, dx \) --- Explanation: This is an integral calculus problem requiring the integration of the product of \(x\) and \(\arctan(x^2)\). Possible methods for solving this could include integration by parts or trigonometric substitution.
1. \( \int x \arctan(x^2) \, dx = \frac{1}{2} x^2 \arctan(x^2) - \frac{1}{4} \ln(1 + x^4) + C \) This equation represents the integral of the function \( x \arctan(x^2) \) with respect to \( x \). The result on the right side involves a combination of the arctangent function and a logarithmic function, both influenced by powers of \( x \), along with the constant of integration \( C \). The solution is shown in red, emphasizing its importance in the context of integration techniques.
Transcribed Image Text:1. \( \int x \arctan(x^2) \, dx = \frac{1}{2} x^2 \arctan(x^2) - \frac{1}{4} \ln(1 + x^4) + C \) This equation represents the integral of the function \( x \arctan(x^2) \) with respect to \( x \). The result on the right side involves a combination of the arctangent function and a logarithmic function, both influenced by powers of \( x \), along with the constant of integration \( C \). The solution is shown in red, emphasizing its importance in the context of integration techniques.
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