laplace transform x^3e^{-x^2}

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

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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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laplace transform x³e^−x²

Solution

−1

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L{e^−x²x³}

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

For x³e^−x²: f(x)=e^−x², k=3

=(−1)³d³ds³ (L{e^−x²})

L{e^−x²}: √π2 e^s²4erfc(s2 )

=(−1)³

=−1

Solve instead

inverse laplace x³e^−x²

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