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Inverse Laplace Transform of a Rational Function Sum

Differential equations warmup

Find \[ \mathcal{L}^{-1}\left(\frac{8}{s+5} + \frac{7}{s^2+3}\right). \]
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What this problem tests

Tests the ability to use linearity and recognize standard Laplace transform pairs, including adjusting constants to match the required forms.

This is a standard introductory problem in a differential equations course covering Laplace transforms.

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