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Evaluate the following integrals. Use only the variables "u" (and "v" if applicable) in your substitutions. 1. S dx Vx+2 2. S* dx Vx-9 3. ſešx tan e5x dx

Evaluate the following integrals. Use only the variables "u" (and "v" if applicable) in your substitutions. 1. S dx Vx+2 2. S* dx Vx-9 3. ſešx tan e5x dx

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 54E
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 please answer number  3 and follow the format of sample solution (include the rules/techniques used)  

Evaluate the following integrals. Use only the variables "u" (and "v" if applicable) in your substitutions. 1. S dx Vx+2 2. S dx 3. ſesx tan e 5x dx 4. S(x² – 1) Vx + 4 dx 5. S dx
Transcribed Image Text:Evaluate the following integrals. Use only the variables "u" (and "v" if applicable) in your substitutions. 1. S dx Vx+2 2. S dx 3. ſesx tan e 5x dx 4. S(x² – 1) Vx + 4 dx 5. S dx
Sample solution with steps: Evaluate the integral. 3-2 sin x dx 3x+2 cos x Step 1: Rewrite the equation in the form f(u)du. Let u = 3x + 2 cos x du = (3 – 2sin x) dx Substitute u and du on the original equation. 3-2 sinx 3x+2 cos x dx = J (+2 cos x ) (3 – 2 sin x)dx - SC) du Step 2: Integrate S () du. Use the integration rule: S = In x + C S) du = In u + C Step 3: Substitute back u = 3x + 2 cos x. In u + C = In (3x + 2 cos x) + C 3-2 sin x Therefore, S dx = In (3x +2 cos x) + C 3x+2 cos x
Transcribed Image Text:Sample solution with steps: Evaluate the integral. 3-2 sin x dx 3x+2 cos x Step 1: Rewrite the equation in the form f(u)du. Let u = 3x + 2 cos x du = (3 – 2sin x) dx Substitute u and du on the original equation. 3-2 sinx 3x+2 cos x dx = J (+2 cos x ) (3 – 2 sin x)dx - SC) du Step 2: Integrate S () du. Use the integration rule: S = In x + C S) du = In u + C Step 3: Substitute back u = 3x + 2 cos x. In u + C = In (3x + 2 cos x) + C 3-2 sin x Therefore, S dx = In (3x +2 cos x) + C 3x+2 cos x
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