преобразование Лапласа xcos(2x)

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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

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laplace transform xcos(2x)

Solution

−−s²+4(s²+4)²

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Solution steps

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L{xcos(2x)}

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

For xcos(2x): f(x)=cos(2x), k=1

=(−1)¹dds (L{cos(2x)})

L{cos(2x)}: ss²+4

dds (ss²+4 )=−s²+4(s²+4)²

=(−1)¹−s²+4(s²+4)²

=−−s²+4(s²+4)²

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

преобразование Лапласа xcos(2x)

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