3. (Trigonometric substitution and partial fractions) In this question, you are asked to solve the integral S √²+2x+2 dx (x € (0, ∞)), which involves multiple steps. Answer the following questions to obtain the solution. de. i. Complete the square, use a substitution, and a trigonometric substitution to convert the integral into 5 sin² (9) cos(8) ii. Use the substitution v = : sin(₹) to convert the integral into S²(1-²) dv. iii. Use partial fractions to show that the integral equals √3-1 √²+2x+2 dx. x²+2x+1 iv. Evaluate /1+(1+x)² 1+x +In √1+(1+x)²+1+x √1+(1+x)²-1-x +C
3. (Trigonometric substitution and partial fractions) In this question, you are asked to solve the integral S √²+2x+2 dx (x € (0, ∞)), which involves multiple steps. Answer the following questions to obtain the solution. de. i. Complete the square, use a substitution, and a trigonometric substitution to convert the integral into 5 sin² (9) cos(8) ii. Use the substitution v = : sin(₹) to convert the integral into S²(1-²) dv. iii. Use partial fractions to show that the integral equals √3-1 √²+2x+2 dx. x²+2x+1 iv. Evaluate /1+(1+x)² 1+x +In √1+(1+x)²+1+x √1+(1+x)²-1-x +C
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...
Related questions
Question
Transcribed Image Text:3. (Trigonometric substitution and partial fractions) In this question, you are asked to solve the integral
dx (x = (0, ∞)), which involves multiple steps. Answer the following questions to obtain the solution.
S
√x²+2x+2
x²+2x+1
i. Complete the square, use a substitution, and a trigonometric substitution to convert the integral into 5 sin²(0) cos(0) -do.
sin() to convert the integral into [ ²(1-²) dv.
ii. Use the substitution v
=
iii. Use partial fractions to show that the integral equals
iv. Evaluate
√3-1 √√√x²+2x+² dx.
x²+2x+1
1+(1+x)²
1+x
1
+ In
/1+(1+x)²+1+x
√1+(1+x)²− -1-x
+ C
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
In the last part, wouldn't the range be calculated by the
Solution
by Bartleby ExpertSimilar questions
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning