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Evaluate the indefinite integral. x² dx 1 + x6

Evaluate the indefinite integral. x² dx 1 + x6

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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This question has several parts that must be completed sequentially. If you skip a part of the question, you will nc skipped part. Tutorial Exercise Evaluate the indefinite integral. x2 dx 1 + x6 Step 1 We must decide what to choose for u. If u = f(x), then du = f '(x) dx, and so it is helpful to look for some x2 1 + x6 expression in dx for which the derivative is also present, though perhaps missing a constant factor. Finding u in this integral is a little trickier than in some others. which is not We see that 1+ x° is part of this integral, but the derivative of 1 + x° is present in the integrand. However, notice that the x in the numerator is close to the derivative of x, which is
Transcribed Image Text:This question has several parts that must be completed sequentially. If you skip a part of the question, you will nc skipped part. Tutorial Exercise Evaluate the indefinite integral. x2 dx 1 + x6 Step 1 We must decide what to choose for u. If u = f(x), then du = f '(x) dx, and so it is helpful to look for some x2 1 + x6 expression in dx for which the derivative is also present, though perhaps missing a constant factor. Finding u in this integral is a little trickier than in some others. which is not We see that 1+ x° is part of this integral, but the derivative of 1 + x° is present in the integrand. However, notice that the x in the numerator is close to the derivative of x, which is
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