inverse of laplace e^xx

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for expand factor rationalize

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inverse laplace e^xx

Solution

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Solution steps

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L⁻¹{e^xx}

Apply inverse transform rule: if L⁻¹{F(s)}=f(t) then L⁻¹{sF(s)}=ddt f(t)+f(0)

For e^xx: F(x)=e^x

=ddt (L⁻¹{e^x})+L⁻¹{e^x}(0)

L⁻¹{e^x}: δ(t+1)

Evaluate δ(t+1) at point 0=Undefined

=Undefined

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

inverse of laplace e^xx

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