How do you evaluate the integral $int 1/x dx$ from 1 to $oo$ ?

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Answer 1 · 2016-08-21T03:06:41

The integral does not converge.

Note that $1/x$ is the derivative of $ln(x)$ , so the integral $int1/xdx=ln(x)+C$ .

In this case:

$int_1^oo1/xdx=[ln(x)]_1^oo$

Now evaluating, and using a limit for infinity:

$=lim_(xrarroo)ln(x)-ln(1)$

$ln(1)=0$ and the limit approaches infinity, thus the integral does not converge.

$=oo$

If you don't understand why $lim_(xrarroo)ln(x)=oo$ , take a look at the graph of $ln(x)$ :

graph{lnx [-11.39, 39.92, -12.47, 13.19]}

The function steadily rises.

How do you evaluate the integral int 1/x dxint 1/x dx from 1 to oooo?