1/3(x– 1) dx VI+x² - 1 dx

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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Having issues w/ both a and b. I think it's supposed to be a u substitution problem but the square root is throwing me for a loop when I try and start both of them.

The image contains two integral expressions:

1. The first integral is \(\int \frac{x^{1/3}(x-1)}{\sqrt{x}} \, dx\).

2. The second integral is \(\int \frac{\sqrt{x} + x^2 - 1}{x} \, dx\).

These integrals involve algebraic expressions with fractional exponents and radicals, which represent a common type of problem in calculus. The expressions indicate the need for techniques such as substitution or integration by parts to find the antiderivative, depending on the complexity and form. No graphs or diagrams are present in the image.
Transcribed Image Text:The image contains two integral expressions: 1. The first integral is \(\int \frac{x^{1/3}(x-1)}{\sqrt{x}} \, dx\). 2. The second integral is \(\int \frac{\sqrt{x} + x^2 - 1}{x} \, dx\). These integrals involve algebraic expressions with fractional exponents and radicals, which represent a common type of problem in calculus. The expressions indicate the need for techniques such as substitution or integration by parts to find the antiderivative, depending on the complexity and form. No graphs or diagrams are present in the image.
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