(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

OK, this is something that stumped me.

2. Relevant equations

[itex]\int_{}^{}{\frac{dZ}{ A^{2}-Z^{2}}} = - \int_{}^{}{\frac{dZ}{ Z^{2}-A^{2} }}[/itex]

Right?

[itex]\int_{}^{}{\frac{dZ}{ A^{2}-Z^{2} }}=\; \frac{1}{2A}\ln \left\{ \frac{A+Z}{A-Z} \right\}+\mbox{C}[/itex]

[itex]\int_{}^{}{\frac{dZ}{ Z^{2}-A^{2} }}=\; \frac{1}{2A}\ln \left\{ \frac{Z-A}{Z+A} \right\}+\mbox{C}[/itex]

3. The attempt at a solution

But I don't see how,

[itex]\frac{1}{2A}\ln \left\{ \frac{A+Z}{A-Z} \right\}+\mbox{C} = - \frac{1}{2A}\ln \left\{ \frac{Z-A}{Z+A} \right\}+\mbox{C}[/itex]

It should be,

[itex]\frac{1}{2A}\ln \left\{ \frac{A+Z}{A-Z} \right\}+\mbox{C} = - \frac{1}{2A}\ln \left\{ \frac{A-Z}{A+Z} \right\}+\mbox{C}[/itex]

No?

I derived both (OK one of them; the other I just read from the textbook), the integrations "check out", but I don't understand why!? Why the term inside "ln" is "multiplied by -1"?

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# Homework Help: Question regarding certain standard integrals.

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