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- schmisoLv 71 decade agoFavorite Answer
Just expand your expression such that you can use the the transformation formula for integer powers of t which is:
ℒ{ tⁿ } = n!/sⁿ⁺¹
ℒ{ (t² + 1)² }
= ℒ{ t⁴ + 2∙t²+ 1 }
= ℒ{ t⁴ } + 2∙ℒ{ t² } + ℒ{ 1 }
= 4!/s⁵ + 2∙2!/s³ + 0!/s
= 24/s⁵ + 4/s³ + 1/s
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