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

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trasformata di laplace cosh²(x)

Solution

12s +s2(s²−4)

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L{cosh²(x)}

Usare l'identità seguente: cosh²(x)=12 +cosh(2x)12

=L{12 +cosh(2x)12 }

Utilizzare la proprietà di linearità della trasformata di Laplace:
Per le funzioni f(t), g(t) e le costanti a, b: La·f(t)+b·g(t)\=a·Lf(t)\+b·Lg(t)\

=L{12 }+12 L{cosh(2x)}

L{12 }: 12s

L{cosh(2x)}: ss²−4

=12s +12 · ss²−4

Raffinare 12s +12 · ss²−4 : 12s +s2(s²−4)

=12s +s2(s²−4)

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trasformata di laplace inversa cosh²(x)

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

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