The common way to do this will be like:
syms r d y;
f= (r^(r+d))*( d^2 * y^2)/( (d+r)^2*d^3 )
F = int(f, y) % Calculate undefinite integral using variable y
G= int(F,x) % and again using x
a=int(F, x, -15, 15) % for definite integration
Good luck :)
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