Question

find the inverse laplace transform of 1/(s+3)^5​

Answer 1

Step-by-step explanation:

Given:

$\frac{1}{ {(s+3)}^{5} }$

To find: Compute inverse Laplace of given function.

Solution:

Formula used:

$\bold{\red{ {£}^{ - 1} \left( \frac{1}{(s - a)^{n} } \right) = \frac{ {e}^{at} {t}^{n - 1} }{(n - 1)!} }}$

Use the above formula

${£}^{ - 1} \left( \frac{1}{(s +3)^{5} } \right) = \frac{ {e}^{-3t} {t}^{5 - 1} }{(5- 1)!} \\ \\ {£}^{ - 1} \left( \frac{1}{(s +3)^{5} } \right) = \frac{ {e}^{-3t} {t}^{4} }{(4)!} \\ \\ {£}^{ - 1} \left( \frac{1}{(s +3)^{5} } \right) = \frac{ {e}^{-3t} {t}^{4} }{24}$

Final answer:

$\bold{\green{{£}^{ - 1} \left( \frac{1}{(s +3)^{5} } \right) = \frac{ {e}^{-3t} {t}^{4} }{24}}}$

Hope it helps you.

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