why it is diverge

According to Mathcad:

and Wolfram Alpha won't evaluate it.

.

Here is the graph.

https://www.desmos.com/calculator/orgvwef1o3

Why does what you circled =0 ??

What does diverge and converge mean?

Thinking about what they 'may' mean this doesn't really do either does it?

I know I am out of my depth here. 

I guess I am hoping someone will teach me something that is easy to learn. (Well one can dream)  :)  

Like Melody, I'm on shaky ground here....so.....you might have to take this with a grain of salt....

By the Integral Test, the function in the integrand must be eventually positive and decreasing on the interval of interest - in this case, 0 to ∞.

Here's the graph of  y = cos(x)*e^(-sin(x))

.....https://www.desmos.com/calculator/ho13rj5sjr

Note that this function is not eventually positive and decreasing on the interval (it is periodic).....thus.....the integral diverges

That's my two cents worth.....

Alan???  heureka???....to the rescue???