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

[tex] \int \frac {2+z^{-1}}{z^{2}} dz [/tex]

3. The attempt at a solution

Let:

[tex] u = 2 +z^{-1} [/tex]

[tex] du = -z^{-2} dz [/tex]

[tex] dz = -z^{2} du [/tex]

so now its

[tex] \int \frac {u}{z^{2}} (-z^{2}) du [/tex]

[tex] \int \frac {(u)(-z^{2})}{z^{2}} du [/tex]

[tex] \int (u)(-1) du [/tex]

and then the antiderivative of u*(-1) is

[tex] -\frac{1}{2}(2+z^{-1})^{2} + C [/tex]

right? The answer in the book is:

[tex] -2z^{-1}-\frac{1}{2}z^{-2} + C [/tex]

I don't see anywhere that I went wrong....

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# Homework Help: Indefinite Integration by exchange of variables

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