Integration was this (idk if lemmy renders latex):
int_0^1{x^{-1} (1-x)^{n-1}} dx
[
\int_0^1 {x^{-1} (1-x)^{n-1}}dx
]
Text: finite integration from 0 to 1 of function x to power negative one, (1-x) to the power (n-1).
The limit at 0 goes to infinity that’s why there is no solution. But deepseek kept trying different method reaching a conclusion that it can’t be solved then then trying different approach.
About the closed form, the function without closed form was that function multiplied by x^y (1-x)^y .
int_0^1{x^{y-1} (1-x)^{n-y-1}} dx
The first one is a case where y=0. Unless y=0 or n, you have integration, just not a closed form. You can plot the function to see it as well. You’d have to try different values of y and n for it to actually plot something though.
What was the integral and what form does a solution take when there’s no closed form?
I’m curious because I used to know but forgot most of calculus at this point.
Integration was this (idk if lemmy renders latex):
int_0^1{x^{-1} (1-x)^{n-1}} dx[ \int_0^1 {x^{-1} (1-x)^{n-1}}dx ]
Text: finite integration from 0 to 1 of function x to power negative one, (1-x) to the power (n-1).
The limit at 0 goes to infinity that’s why there is no solution. But deepseek kept trying different method reaching a conclusion that it can’t be solved then then trying different approach.
About the closed form, the function without closed form was that function multiplied by x^y (1-x)^y .
int_0^1{x^{y-1} (1-x)^{n-y-1}} dxThe first one is a case where y=0. Unless y=0 or n, you have integration, just not a closed form. You can plot the function to see it as well. You’d have to try different values of y and n for it to actually plot something though.