%% formulation
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\begin{document}
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\begin{align*}
\min_{u(t)} \quad & \int_{0}^{t_f} \left[ x^2 + u^2 \right] \mathrm{d}t \\
\text{subject to:} \quad & \dot{x} = -x^3 + u \\
& x(0) = 1.5 \\
& x(t_f) = 1
\end{align*}
}}
\end{document}

%% solution