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laplace transformation sin^3(x)

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

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laplace transform sin³(x)

Solution

6(s²+9)(s²+1)

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Solution steps

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L{sin³(x)}

Rewrite using trig identities

L{−14 sin(3x)+34 sin(x)}

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

=−14 L{sin(3x)}+34 L{sin(x)}

L{sin(3x)}: 3s²+9

L{sin(x)}: 1s²+1

=−14 · 3s²+9 +34 · 1s²+1

Simplify −14 · 3s²+9 +34 · 1s²+1 : 6(s²+9)(s²+1)

=6(s²+9)(s²+1)

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inverse laplace sin³(x)

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

laplace transformation sin^3(x)

Solution

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