laplace transform e^x+x^e

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laplace transform e^x+x^e

Solution

1s−1 +Γ(e+1)s^e+1

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Solution steps

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L{e^x+x^e}

Use the linearity property of Laplace Transform:
For functions f(t), g(t) and constants a, b: L{a·f(t)+b·g(t)}=a·L{f(t)}+b·L{g(t)}

=L{e^x}+L{x^e}

L{e^x}: 1s−1

L{x^e}: Γ(e+1)s^e+1

=1s−1 +Γ(e+1)s^e+1

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inverse laplace e^x+x^e

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+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
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laplace transform e^x+x^e

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