How to do symbolic integration

%% I am unable to get the result. Thank you so much in advance

clc;
clear;
syms omega x n m 
% assuming omega::real,omega>0,m::integer,m>0,n::integer,n>0;
fun=int(cos(atan(1,x))^m*sin(omega*x)/(1+x^2)^((n)/2+1),x,0,Inf);

Answer 1

[Star Strider]

It apparently does not have a symbolic solution (this is not uncommon).

It does have a piecewise closed-form solution, at least over some regions, and one option would be to numerically integrate it (although that could have problems as well) —

syms omega x n m real
sympref('AbbreviateOutput',false);
assume(m,'integer')
assumeAlso(m,'positive')
assume(n,'integer')
assumeAlso(n,'positive')
assume(omega,'positive')
% assuming omega::real,omega>0,m::integer,m>0,n::integer,n>0;
integrand = cos(atan(1,x))^m*sin(omega*x)/(1+x^2)^((n)/2+1)

integrand = 

integrand = simplify(integrand, 500)

integrand = 

fun=int(integrand,x,0,Inf)

fun = 

nfun = matlabFunction(integrand)                                    % Anonymous Function Argument To 'integral'

nfun = function_handle with value:
    @(m,n,omega,x)x.^m.*sin(omega.*x).*(x.^2+1.0).^(m.*(-1.0./2.0)-n./2.0-1.0)

This likely as good as it gets.

.

[gourav pandey]

thank you..it helped me

[Star Strider]

My pleasure!

Answer 2

[KSSV]

Try substituing the values of m and n.

syms omega  positive real
% syms n m positive integer 
syms x 
% assuming omega::real,omega>0,m::integer,m>0,n::integer,n>0;
m = 5 ; n = 4 ;
fun=int(cos(atan(1,x))^m*sin(omega*x)/(1+x^2)^((n)/2+1),x,0,Inf)

fun = 

[gourav pandey]

Hii,

I have some restriction due to which i can't substitute the values on omega, m, and n. Is there any other way to integrate the above expression.