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If you do not know what substitution to make, try reducing the inte- gral step by step, using a trial substitution to simplify the integral a bit and then another to simplify it some more. You will see what we mean if you try the sequences of substitutions in Exercises 67 and 68. 18 tan²x sec² x dx (2 + tan³ x)² 67. a. u = tan x, followed by v = ư, then by w = 2 + v tanx, followed by v = 2 + u c. u = 2 + tan³ x b. и %3D V1 + sin² (x – 1) sin (x – 1) cos (x – 1) dx 68. a. u = x – 1, followed by v = sin u, then by w = 1 + v² b. u = sin (x – 1), followed by v = 1 + ư с. и %3D 1 + sin?(x — 1)

If you do not know what substitution to make, try reducing the inte- gral step by step, using a trial substitution to simplify the integral a bit and then another to simplify it some more. You will see what we mean if you try the sequences of substitutions in Exercises 67 and 68. 18 tan²x sec² x dx (2 + tan³ x)² 67. a. u = tan x, followed by v = ư, then by w = 2 + v tanx, followed by v = 2 + u c. u = 2 + tan³ x b. и %3D V1 + sin² (x – 1) sin (x – 1) cos (x – 1) dx 68. a. u = x – 1, followed by v = sin u, then by w = 1 + v² b. u = sin (x – 1), followed by v = 1 + ư с. и %3D 1 + sin?(x — 1)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 80E
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If you do not know what substitution to make, try reducing the inte- gral step by step, using a trial substitution to simplify the integral a bit and then another to simplify it some more. You will see what we mean if you try the sequences of substitutions in Exercises 67 and 68. 18 tan²x sec² x dx (2 + tan³ x)² 67. a. u = tan x, followed by v = ư, then by w = 2 + v tanx, followed by v = 2 + u c. u = 2 + tan³ x b. и %3D V1 + sin² (x – 1) sin (x – 1) cos (x – 1) dx 68. a. u = x – 1, followed by v = sin u, then by w = 1 + v² b. u = sin (x – 1), followed by v = 1 + ư с. и %3D 1 + sin?(x — 1)
Transcribed Image Text:If you do not know what substitution to make, try reducing the inte- gral step by step, using a trial substitution to simplify the integral a bit and then another to simplify it some more. You will see what we mean if you try the sequences of substitutions in Exercises 67 and 68. 18 tan²x sec² x dx (2 + tan³ x)² 67. a. u = tan x, followed by v = ư, then by w = 2 + v tanx, followed by v = 2 + u c. u = 2 + tan³ x b. и %3D V1 + sin² (x – 1) sin (x – 1) cos (x – 1) dx 68. a. u = x – 1, followed by v = sin u, then by w = 1 + v² b. u = sin (x – 1), followed by v = 1 + ư с. и %3D 1 + sin?(x — 1)
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