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Express the integrand as a sum of partial fractions and evaluate the integral. 64 dx x-16x |3 4 O A. - +2 In |x- 4|+2 In |x+ 4| + C O B. 4 In |x| - 2 In |x - 4| - 2 In |x+ 4|+C Oc. -4 In |x| + i tan + C OD. -4 In |x| + 2 In |x – 4| +2 In |x +4| +C

Express the integrand as a sum of partial fractions and evaluate the integral. 64 dx x-16x |3 4 O A. - +2 In |x- 4|+2 In |x+ 4| + C O B. 4 In |x| - 2 In |x - 4| - 2 In |x+ 4|+C Oc. -4 In |x| + i tan + C OD. -4 In |x| + 2 In |x – 4| +2 In |x +4| +C

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 65E
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**Problem:** Express the integrand as a sum of partial fractions and evaluate the integral. \[ \int \frac{64 \, dx}{x^3 - 16x} \] **Options:** A. \(-\frac{4}{x} + 2 \ln |x - 4| + 2 \ln |x + 4| + C\) B. \(4 \ln |x| - 2 \ln |x - 4| - 2 \ln |x + 4| + C\) C. \(-4 \ln |x| + \frac{1}{4} \tan^{-1}\left(\frac{x}{4}\right) + C\) D. \(-4 \ln |x| + 2 \ln |x - 4| + 2 \ln |x + 4| + C\)
Transcribed Image Text:**Problem:** Express the integrand as a sum of partial fractions and evaluate the integral. \[ \int \frac{64 \, dx}{x^3 - 16x} \] **Options:** A. \(-\frac{4}{x} + 2 \ln |x - 4| + 2 \ln |x + 4| + C\) B. \(4 \ln |x| - 2 \ln |x - 4| - 2 \ln |x + 4| + C\) C. \(-4 \ln |x| + \frac{1}{4} \tan^{-1}\left(\frac{x}{4}\right) + C\) D. \(-4 \ln |x| + 2 \ln |x - 4| + 2 \ln |x + 4| + C\)
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