Integral of the product of integrals

I1 = integral [f1(x,y), x, a, b]
I2 = integral [f2(x,y), x, a, b]
I3 = integral [f3(x,y), x, a, b]

integral(I1*I2*I3, y, c, d)

Note that a,b,c,d are constant. Integrals have no analytical solution.

Answer 1

[Matt J]

I=@(y,f) integral( @(x)f(x,y), a, b);

I123=@(y) I(y,f1) .* I(y,f2) .* I(y,f3);


integral(I123, c, d)

[Morteza]

f1= @(y, teta) y.*exp(teta.^2);
f2=@(y, teta) y.*exp(teta.^3);
f3=@(y, teta) y.*exp(teta.^4);

I=@(teta,f) integral( @(y)f(y, teta), 0, 50);
I123=@(teta) I(teta,f1) .* I(teta,f2) .* I(teta,f3);

integral(I123, 0, 50 ) 

This is an example based on your code. Error:

Error using integralCalc/finalInputChecks (line 515)

Output of the function must be the same size as the input. If FUN is an array-valued integrand,

set the 'ArrayValued' option to true.

[Torsten]

integral(I123, 0, 50,'ArrayValued',true ) 

And you shouldn't integrate exp(teta^2),exp(teta^3) or exp(teta^4) up to teta = 50.