Apparent discrepancy Three different computer algebra

Chapter 7, Problem 58E

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QUESTION:

Apparent discrepancy Three different computer algebra systems give the following results:

\(\int \frac{d x}{x \sqrt{x^{4}-1}}=\frac{1}{2} \cos ^{-1} \sqrt{x^{-4}}=\frac{1}{2} \cos ^{-1} x^{-2}=\frac{1}{2} \tan ^{-1} \sqrt{x^{4}-1}\)

Explain how they can all be correct.

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QUESTION:

Apparent discrepancy Three different computer algebra systems give the following results:

\(\int \frac{d x}{x \sqrt{x^{4}-1}}=\frac{1}{2} \cos ^{-1} \sqrt{x^{-4}}=\frac{1}{2} \cos ^{-1} x^{-2}=\frac{1}{2} \tan ^{-1} \sqrt{x^{4}-1}\)

Explain how they can all be correct.

ANSWER:

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We are here required to solve the apparent discrepancy

 

 

 

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