<transcript><audio_27>instead of a 1 you can use integration parts again but now we integrate the e to the power minus T as first this gives us a minus 1 over s times its power minus TS don't see the power F between 0</transcript><transcript><audio_28>and infinity minus derivative of T to the power ads and I'm still our n minus 1 you can put unfroze integration sign here if you T to the power n minus 1 and you keep your s times 1 over s times its</transcript><transcript><audio_29>power minus TS you can put one of us in front of the integration sign because it doesn't depend on T and here we are for its power minus TS I want you observe it that you get from this part no</transcript><transcript><audio_30>contributions T equals 0 of 0 and on affinity vanishes well because you had to take your real part of s again positive in order to get rid of the integrate integrand on the upper boundary so get rid of the first term</transcript><transcript><audio_31>they observed it what you have left is n of s times the Laplace transform of T to the power n minus 1 so if you have Laplace transform of T to the power n minus 1 you can compute the Laplace</transcript> instead of a 1 you can use integration parts again but now we integrate the e to the power minus T as first this gives us a minus 1 over s times its power minus TS don't see the power F between 0 and infinity minus derivative of T to the power ads and I'm still our n minus 1 you can put unfroze integration sign here if you T to the power n minus 1 and you keep your s times 1 over s times its power minus TS you can put one of us in front of the integration sign because it doesn't depend on T and here we are for its power minus TS I want you observe it that you get from this part no contributions T equals 0 of 0 and on affinity vanishes well because you had to take your real part of s again positive in order to get rid of the integrate integrand on the upper boundary so get rid of the first term they observed it what you have left is n of s times the Laplace transform of T to the power n minus 1 so if you have Laplace transform of T to the power n minus 1 you can compute the Laplace
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