Evaluate the integerals.
`int (e ^(log x))/(x ) dx on (0,oo).`

Answer

To evaluate the integral

\[ \int_0^\infty \frac{e^{\log x}}{x} \, dx, \]

we can follow these steps:

### Step 1: Simplify the integrand
We know that \( e^{\log x} = x \). Therefore, we can rewrite the integrand:

\[ \frac{e^{\log x}}{x} = \frac{x}{x} = 1. \]

### Step 2: Rewrite the integral
Now, substituting this back into the integral, we have:

\[ \int_0^\infty 1 \, dx. \]

### Step 3: Evaluate the integral
The integral of 1 over the interval from 0 to infinity is:

\[ \int_0^\infty 1 \, dx = \lim_{b \to \infty} \int_0^b 1 \, dx = \lim_{b \to \infty} [x]_0^b = \lim_{b \to \infty} (b - 0) = \infty. \]

### Conclusion
Thus, the integral diverges, and we conclude that:

\[ \int_0^\infty \frac{e^{\log x}}{x} \, dx = \infty. \]