Ayuda con este problema de transformada de laplace por favor?

Por tabla se tiene <img src="https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5C%7BF%282t%29%5C%7D%28s%29%3D%5Cdfrac%7B1%7D%7B2%7D%5Cmathcal%7BL%7D%5C%7BF%28t%29%5C%7D%5Cleft%28%5Cdfrac%7Bs%7D%7B2%7D%5Cright%29%5C%5C%20%5C%5C%20%5C%5C%0A%5Cmathcal%7BL%7D%5C%7BF%282t%29%5C%7D%28s%29%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B%28%5Cfrac%7Bs%7D%7B2%7D%29%5E2-%5Cfrac%7Bs%7D%7B2%7D%2B1%7D%7B%282%5Ccdot%5Cfrac%7Bs%7D%7B2%7D%2B1%29%28%5Cfrac%7Bs%7D%7B2%7D-1%29%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Cmathcal%7BL%7D%5C%7BF%282t%29%5C%7D%28s%29%3D%5Cdfrac%7B%5Cfrac%7Bs%5E2%7D%7B4%7D-%5Cfrac%7Bs%7D%7B2%7D%2B1%7D%7B%28s%2B1%29%5E2%28s-2%29%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7B%5Cboxed%7B%5Cmathcal%7BL%7D%5C%7BF%282t%29%5C%7D%28s%29%3D%5Cdfrac%7Bs%5E2-2s%2B4%7D%7B4%28s%2B1%29%5E2%28s-2%29%7D%7D%7D" />.