Is this function Lebesgue integrable or integrable in general?

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Let $\phi:(0, +\infty) \times [0, +\infty) \to R$ be defined by:

$$ \phi(x, t) = \begin{cases} e^{-xt}\frac{\sin{t}}{t} & \quad \text{if } t \neq 0\\ 1 & \quad \text{if } t = 0 \\ \end{cases} $$

How can i show that $\forall \space x \in (0, +\infty), \phi \text{ is Lebesgue integrable w.r.t } t \text{ on } [0, +\infty)$