Question

Find a function f which satisfies the integral equation
Int(bounded from 0 to x) t*f(t)dt = Int(bounded from x to 0)(t^2+1)*f(t)dt +x

Answer 1

Differentiating the equation:

x*f(x)=-(x^2+1)*f(x)+1

f(x)=1/(x^2+x+1)