inverse of laplace (-9x^2-82x-18)/(x+9)

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

☐²

x^☐

√☐

^□√☐

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log_□

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∫

ddx

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

simplify solve for inverse tangent line

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inverse laplace −9x²−82x−18x+9

Solution

−9δ′(t)−δ(t)−9e^−9t

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L⁻¹{−9x²−82x−18x+9 }

Take the partial fraction of −9x²−82x−18x+9 : −9x−1−9x+9

=L⁻¹{−9x−1−9x+9 }

Use the linearity property of Inverse Laplace Transform:
For functions f(s), g(s) and constants a, b: L⁻¹{a·f(s)+b·g(s)}=a·L⁻¹{f(s)}+b·L⁻¹{g(s)}

=−9L⁻¹{x}−L⁻¹{1}−L⁻¹{9x+9 }

L⁻¹{x}: δ′ (t)

L⁻¹{1}: δ(t)

L⁻¹{9x+9 }: 9e^−9t

=−9δ′ (t)−δ(t)−9e^−9t

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

inverse of laplace (-9x^2-82x-18)/(x+9)

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