laplace transform x^23^{-x}

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

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laplace transform x²3^−x

Solution

2(s+ln(3))³

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Solution steps

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L{3^−xx²}

Use Laplace Transform table: L{t^kf(t)}=(−1)^kd^kds^k (L{f(t)})

For x²3^−x: f(x)=3^−x, k=2

=(−1)²d²ds² (L{3^−x})

L{3^−x}: 1s+ln(3)

d²ds² (1s+ln(3) )=2(s+ln(3))³

=(−1)²2(s+ln(3))³

=2(s+ln(3))³

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inverse laplace x²3^−x

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

laplace transform x^23^{-x}

Solution

Solution steps

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