been having trouble getting results in CAS system

[webmasterpdx]

Actually,

int((1+(dy/dx)^2)^(1/2),x,0,1) giving 1 as an answer is also wrong.

y=(1-x^n)^(1/n) is y^n=1^n-x^n or x^n+y^n=1^n

For n=2, this is the equation of a circle with radius 1.
I'm only interested in quadrant 1 (Q1), integrating from 0 to 1.

This means for n=2, L is quarter the circumference of a circle of radius 1.
L=2*pi*r/4 = 2*pi/4 = pi/2 = 1.57

For n=infinity, it becomes a square pulse, so L = 1+1 = 2

So, for n=3, L must be somewhere between 1.57 and 2.....around 1.7 or so, not 1 as in previous post CAS system.

So, if I can figure this out in my head, there must be a mathematical way to determine L for n=3.

Any ideas?

Thanks
-Donald