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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![Certainly! Here's the transcription of the image as it would appear on an educational website, related to integrals:
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**Reference Pages: Table of Integrals**
**Forms Involving \(a + bu\)**
47. \(\int \frac{du}{a + bu} = \frac{1}{b} \ln |a + bu - a \ln |a + bu|| + C\)
48. \(\int \frac{u^2 \, du}{a + bu} = \frac{1}{2b^2} \left[(a + bu)^2 - 4a(a + bu) + 2a^2 \ln |a + bu| \right] + C\)
49. \(\int \frac{du}{u(a + bu)} = \frac{1}{a} \ln \left| \frac{a + bu}{u} \right| + C\)
50. \(\int \frac{du}{u^2(a + bu)} = - \frac{1}{a} \left[ \frac{1}{u} + \frac{b}{a^2} \ln |a + bu| \right] + C\)
51. \(\int \frac{u \, du}{(a + bu)^2} = \frac{a}{b^3} + \frac{u}{a(a + bu)} + C\)
52. \(\int \frac{1}{b^2} \left[ - \frac{1}{a(b + bu)} + \frac{1}{a^2} \ln |a + bu| \right] + C\)
53. \(\int \frac{u^2 \, du}{(a + bu)^3} = \frac{1}{b^3} \left[ \frac{a}{b^2} - \frac{a^2 - 2a}{a^2(b + bu)} \right] + C\)
54. \(\int \frac{u \sqrt{a + bu} \, du}{a + bu} = \frac{2}{15b^2} (3bu - 2a)(a + bu)^{3/2} + C\)
55. \(\int \frac{u \, du}{\sqrt{a + bu}} = \frac](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8df10466-bb36-424d-be07-c1f915d82bc7%2F55373f4b-15c7-4b45-958a-524df19768d3%2Fxznj19r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here's the transcription of the image as it would appear on an educational website, related to integrals:
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**Reference Pages: Table of Integrals**
**Forms Involving \(a + bu\)**
47. \(\int \frac{du}{a + bu} = \frac{1}{b} \ln |a + bu - a \ln |a + bu|| + C\)
48. \(\int \frac{u^2 \, du}{a + bu} = \frac{1}{2b^2} \left[(a + bu)^2 - 4a(a + bu) + 2a^2 \ln |a + bu| \right] + C\)
49. \(\int \frac{du}{u(a + bu)} = \frac{1}{a} \ln \left| \frac{a + bu}{u} \right| + C\)
50. \(\int \frac{du}{u^2(a + bu)} = - \frac{1}{a} \left[ \frac{1}{u} + \frac{b}{a^2} \ln |a + bu| \right] + C\)
51. \(\int \frac{u \, du}{(a + bu)^2} = \frac{a}{b^3} + \frac{u}{a(a + bu)} + C\)
52. \(\int \frac{1}{b^2} \left[ - \frac{1}{a(b + bu)} + \frac{1}{a^2} \ln |a + bu| \right] + C\)
53. \(\int \frac{u^2 \, du}{(a + bu)^3} = \frac{1}{b^3} \left[ \frac{a}{b^2} - \frac{a^2 - 2a}{a^2(b + bu)} \right] + C\)
54. \(\int \frac{u \sqrt{a + bu} \, du}{a + bu} = \frac{2}{15b^2} (3bu - 2a)(a + bu)^{3/2} + C\)
55. \(\int \frac{u \, du}{\sqrt{a + bu}} = \frac
Transcribed Image Text:**Problem 3:**
Find \(\int \frac{x \, dx}{x+1}\) by first dividing.
Then use Formula #47 to find \(\int \frac{x \, dx}{x+1}\).
Do your results agree?
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