Help to understand manipulating of limit in integral

[spock]

I don't understand how to get "the integral from 0 to ln x with y(x) as term" to "the integral from 1 to x with y(x)/x as term".

Help me to understand. What is the name for the manipulation that change the limits in an integral.

 

[Reynolds]

I don't understand how to get "the integral from 0 to ln x with y(x) as term" to "the integral from 1 to x with y(x)/x as term".

Help me to understand. What is the name for the manipulation that change the limits in an integral.

Hi, Spock! The typical way to manipulate the borders and the function under the integral would be to use integration by substitution method.
Using e^x you can reach desired borders, but I am not sure for the function under the integral sign.
More precisely, i am not sure that you can go from one to other integral (in this case).
Try using i.e. y(x) = x^{21} and than calculate both of integrals, do you get the same?