Our EXP functions are made in the following way: - Any constant $ \in \Bbb R$ is a EXP - $X \in \Bbb R$ is a EXP - $sin( g(x))$, $cos( g(x))$ - $tan( g(x))$ are EXP, $g(x)$ is a EXP and $g(x) \neq \frac\pi 2 + k\pi, k \in \Bbb Z $ - $sqrt( g(x))$ is a EXP, $g(x)$ is a EXP and $g(x) \geq 0$ - $pow( f(x),g(x))$ is a EXP, $g(x),f(x)$ are EXP - $exp(g(x))$ is a EXP - $ln(f(x))$ is a EXP, $f(x) \gt 0$ is a EXP - $f(x)+g(x)$ is a EXP, $g(x),f(x)$ are EXP - $f(x)-g(x)$ is a EXP, $g(x),f(x)$ are EXP - $f(x)*g(x)$ is a EXP, $g(x),f(x)$ are EXP - $f(x)/g(x)$ is a EXP, $g(x),f(x)$ are EXP - $f'(f(x))$ is a EXP (derivative) What I want to know, is if there's an algorithm that, given $f(x) \in EXP$ can say: - **Yes:** iff there exist a $g(x)$ such that $g'(x) = f(x)$ and $g(x) \in EXP$ - **No:** otherwise - **Always halt**