**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. $-4 \ln |x| + 2 \ln |x - 4| + 2 \ln |x + 4| + C$

Answered: Image /qna-images/answer/300554c9-8a15-453a-9075-3d3fdcc6456e.jpg

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

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.4: Fractional Expressions

Problem 65E

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Question

**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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