How to integrate a complicated function?

Hello,

I am trying to integrate the following function using 'int' but it is not working. Is there any other way to integrate it?

clear
clc
close all
syms z L EI n kd 
x=sin(n*pi*z/L);
x1=simplify(diff(x,z));
x2=simplify(diff(x1,z));
k1=int(EI*x2^2,z,[0,L]);
k3=int(x1^2,z,[0,L]);
k2=kd*int((z)^.5*x^2,z,[0,L])

k2 = 

[Sam Chak]

Hi @SAM,

I see and .

So I guess this problem is related to the Euler–Bernoulli or the Timoshenko–Ehrenfest beam theory.

If this is boundary value problem, you can try solving it using the bvp4c() function.

[SAM]

@Sam Chak my ode here is 4th order, it is actually a pile's buckling equation where I am trying to solve for N. Is there another function to solve for 4th order?

Answer 1

[Torsten]

https://www.wolframalpha.com/input?i=integration&assumption=%7B%22C%22%2C+%22integration%22%7D+-%3E+%7B%22Calculator%22%7D&assumption=%7B%22F%22%2C+%22Integral%22%2C+%22rangestart%22%7D+-%3E%220%22&assumption=%7B%22F%22%2C+%22Integral%22%2C+%22integrand%22%7D+-%3E%22Sqrt%5Bx%5D*%28Sin%5BPi*n*x%2FL%5D%29%5E2%22&assumption=%7B%22F%22%2C+%22Integral%22%2C+%22rangeend%22%7D+-%3E%22L%22

https://uk.mathworks.com/help/symbolic/sym.fresnels.html

"l" seems to be "L" in the result presentation.