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29. | (3x¹/³ + 4x² +6) dx

29. | (3x¹/³ + 4x² +6) dx

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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Question 25 and 29. Show all work, thank you! Answers are given.
**Transcription for Educational Website:** 19. \( e^x + C \) 21. \( \tan^{-1} s + C \) 23. \( \frac{1}{2}x^6 - \frac{1}{2}x^{10} + C \) 25. \( \frac{8}{3}x^{3/2} - 8x^{1/2} + C \) 27. \( \frac{25}{3}s^3 + 15s^2 + 9s + C \) 29. \( \frac{9}{4}x^{4/3} + 6x^{2/3} + 6x + C \) 31. \( -x^3 + \frac{11}{2}x^2 + 4x + C \) 33. \( -x^{-3} + 2x + 3x^{-1} + C \) 35. \( x^4 - 3x^2 + C \) **Explanation:** This text contains a list of mathematical expressions, each representing an antiderivative (indefinite integral) of a given function. The constant \( C \) represents the constant of integration, which appears in every result of an indefinite integral. The list includes polynomial expressions and functions involving trigonometric and exponential terms. There are no graphs or diagrams included in the image.
Transcribed Image Text:**Transcription for Educational Website:** 19. \( e^x + C \) 21. \( \tan^{-1} s + C \) 23. \( \frac{1}{2}x^6 - \frac{1}{2}x^{10} + C \) 25. \( \frac{8}{3}x^{3/2} - 8x^{1/2} + C \) 27. \( \frac{25}{3}s^3 + 15s^2 + 9s + C \) 29. \( \frac{9}{4}x^{4/3} + 6x^{2/3} + 6x + C \) 31. \( -x^3 + \frac{11}{2}x^2 + 4x + C \) 33. \( -x^{-3} + 2x + 3x^{-1} + C \) 35. \( x^4 - 3x^2 + C \) **Explanation:** This text contains a list of mathematical expressions, each representing an antiderivative (indefinite integral) of a given function. The constant \( C \) represents the constant of integration, which appears in every result of an indefinite integral. The list includes polynomial expressions and functions involving trigonometric and exponential terms. There are no graphs or diagrams included in the image.
**Indefinite Integrals: Practice Problems** Determine the following indefinite integrals. Check your work by differentiation. 23. \(\int (3x^5 - 5x^9) \, dx\) 24. \(\int (3u^{-2} - 4u^2 + 1) \, du\) 25. \(\int \left( 4\sqrt{x} - \frac{4}{\sqrt{x}} \right) \, dx\) 26. \(\int \left( \frac{5}{t^2} + 4t^2 \right) \, dt\) 27. \(\int (5s + 3)^2 \, ds\) 28. \(\int (5m(12m^3 - 10m)) \, dm\) 29. \(\int (3x^{1/3} + 4x^{-1/3} + 6) \, dx\) 30. \(\int 6\sqrt[3]{x} \, dx\) 31. \(\int (3x + 1)(4 - x) \, dx\)
Transcribed Image Text:**Indefinite Integrals: Practice Problems** Determine the following indefinite integrals. Check your work by differentiation. 23. \(\int (3x^5 - 5x^9) \, dx\) 24. \(\int (3u^{-2} - 4u^2 + 1) \, du\) 25. \(\int \left( 4\sqrt{x} - \frac{4}{\sqrt{x}} \right) \, dx\) 26. \(\int \left( \frac{5}{t^2} + 4t^2 \right) \, dt\) 27. \(\int (5s + 3)^2 \, ds\) 28. \(\int (5m(12m^3 - 10m)) \, dm\) 29. \(\int (3x^{1/3} + 4x^{-1/3} + 6) \, dx\) 30. \(\int 6\sqrt[3]{x} \, dx\) 31. \(\int (3x + 1)(4 - x) \, dx\)
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