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Hint: let u = cx/a, and use (a). (c) Now let ar2 + bx + c be such that a + 0, and b2 – 4ac < 0. Compute: dx J ax2 + bx + c' Hint: Complete the square, and use (b). Exercise 5: (General arctan substitution) Here, we will solve the general case of using an arctan substitution to solve a general inverse quadratic. (a) First, with a E R a constant, solve: dx a2x2 + a² ° (b) Next, with a,ce R constants such that a + 0, solve: dx |a?a2 + c2°

Hint: let u = cx/a, and use (a). (c) Now let ar2 + bx + c be such that a + 0, and b2 – 4ac < 0. Compute: dx J ax2 + bx + c' Hint: Complete the square, and use (b). Exercise 5: (General arctan substitution) Here, we will solve the general case of using an arctan substitution to solve a general inverse quadratic. (a) First, with a E R a constant, solve: dx a2x2 + a² ° (b) Next, with a,ce R constants such that a + 0, solve: dx |a?a2 + c2°

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.1: Rectangular Coordinate Systems
Problem 22E
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Hint: let u = cx/a, and use (a). (c) Now let ar2 + bx + c be such that a + 0, and b2 – 4ac < 0. Compute: dx J ax2 + bx + c' Hint: Complete the square, and use (b).
Transcribed Image Text:Hint: let u = cx/a, and use (a). (c) Now let ar2 + bx + c be such that a + 0, and b2 – 4ac < 0. Compute: dx J ax2 + bx + c' Hint: Complete the square, and use (b).
Exercise 5: (General arctan substitution) Here, we will solve the general case of using an arctan substitution to solve a general inverse quadratic. (a) First, with a E R a constant, solve: dx a2x2 + a² ° (b) Next, with a,ce R constants such that a + 0, solve: dx |a?a2 + c2°
Transcribed Image Text:Exercise 5: (General arctan substitution) Here, we will solve the general case of using an arctan substitution to solve a general inverse quadratic. (a) First, with a E R a constant, solve: dx a2x2 + a² ° (b) Next, with a,ce R constants such that a + 0, solve: dx |a?a2 + c2°
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