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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
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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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
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
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In the last part, wouldn't the range be calculated by the integral change due to the two substitutions to int from 0 to pi/3? 

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