Integral of 1/((lnx)^lnx)

[Nickfytas]

In calculus ii there was the integral of 1/((lnx)^lnx).I've used all the common techniques and I've searched in many websites and didn't find anything and the app that o use for calculations can not calculate it.

 

[ksdhart2]

That's gonna be a real doozy. There's no closed form expression for it, so the best you can do is a numerical approximation, given some bounds. WolframAlpha says of the indefinite integral: "(no result found in terms of standard mathematical functions)"

 

[Nickfytas]

That's gonna be a real doozy. There's no closed form expression for it, so the best you can do is a numerical approximation, given some bounds. WolframAlpha says of the indefinite integral: "(no result found in terms of standard mathematical functions)"

There was a series of that function and to solve it was suggested to us a theorem that puts it in an integral from a number n>0 to infinity and with the limit of that we could understand where the series converges

 

[Dr.Peterson]

In calculus ii there was the integral of 1/((lnx)^lnx).I've used all the common techniques and I've searched in many websites and didn't find anything and the app that o use for calculations can not calculate it.

Please copy the entire problem you are working on, and its context. I wonder if it might be, for example, a definite integral for which you might not need an antiderivative? Or maybe it was in a section on numerical integration?

 

[Nickfytas]

(b) question

 

[Dr.Peterson]

Ok, I was right about it being a definite integral, and within a bigger problem. (This is why we ask for the whole problem.)

So, follow the hint: make the substitution in your integral that will let you use part (a): y = ln(x).

 

[Nickfytas]

Ok, I was right about it being a definite integral, and within a bigger problem. (This is why we ask for the whole problem.)

So, follow the hint: make the substitution in your integral that will let you use part (a): y = ln(x).

Thank you. You've helped a lot