Numerical Integration in Matlab

I wanted to solve a numerical integral of the following equation:

fun = ((x.^4 .* exp(x))) ./ ((exp(x) - 1) .* (exp(x) - 1) );

The limits are from: 0 to Inf

Can anyone ehelp me here?

Thanks in advance.

Answer 1

[Ameer Hamza]

If you have symbolic toolbox

syms x
y = ((x.^4 .* exp(x))) ./ ((exp(x) - 1) .* (exp(x) - 1) );
I = int(y, x, 0, inf)

Result

>> I
I =
(4*pi^4)/15
>> double(I)
ans =
   25.9758

[Raj Patel]

Thanks Ameer. I had one more question.

I could not write the whole problem in Matlab so I have attached a jpg file for you so that you can understand the question.

Also, note that T = logspace(0, 5), and there is a prefactor of T^3 before the integral as well.

I want some help plotting a loglog plot of (T, Cv). Could you please help me?

Thank you.

Raj Patel.

[Ameer Hamza]

Check this code

fun = @(x) (x.^4) ./ (exp(x).*(1 - 1./exp(x)).^2 );
C = @(T) integral(fun, 0, 500/T);

Tv = linspace(0, 1000);
Cv = arrayfun(C, Tv);
loglog(Tv, Cv)

[Raj Patel]

Thanks Ameer. It helped me. Appreciate your efforts.

[Ameer Hamza]

I am glad to be of help!

Answer 2

[Walter Roberson]

integral(fun,0,683)

[Ameer Hamza]

An alternative by rearranging the terms

fun = @(x) (x.^4) ./ (exp(x).*(1 - 1./exp(x)).^2 );
integral(fun, 0, inf)