If $ t $ denotes the greatest integer $ \leq t $, then the value of $ \frac{3(e-1)}{e} \int_{1}^{2} x^{2} e^{[x]+\left[x^{3}\right]} d x $ is equal to [JEE Main 2023, 30 Jan (Shift 1)]

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If \( t \) denotes the greatest integer \( \leq t \), then the value of \( \frac{3(e-1)}{e} \int_{1}^{2} x^{2} e^{[x]+\l…

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