#### Answer

$$P(x)=\frac{1}{x}.$$

#### Work Step by Step

Since $\alpha(x)=e^{\int P(x)dx}$, then
$$ e^{\int P(x)dx}=x\Longrightarrow \int P(x)dx = \ln x.$$
Hence, by differentiation, we have
$$P(x)=\frac{1}{x}.$$

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Published by
W. H. Freeman

ISBN 10:
1464125260

ISBN 13:
978-1-46412-526-3

$$P(x)=\frac{1}{x}.$$

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