trasformata di laplace inversa 2/(x^2+8x+17)

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

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∫

ddx

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

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inverse laplace 2x²+8x+17

Solution

2e^−4tsin(t)

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Solution steps

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L⁻¹{2x²+8x+17 }

Expand 2x²+8x+17 : 2· 1(x+4)²+1

=L⁻¹{2· 1(x+4)²+1 }

Use the constant multiplication property of Inverse Laplace Transform:
For function f(t) and constant a: L⁻¹{a·f(t)}=a·L⁻¹{f(t)}

=2L⁻¹{1(x+4)²+1 }

L⁻¹{1(x+4)²+1 }: e^−4tsin(t)

=2e^−4tsin(t)

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

trasformata di laplace inversa 2/(x^2+8x+17)

Solution

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