d/(dt)(sin^2(t))

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

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≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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部分分数 ∫₀¹x−4x²−5x+6 dx

Solution

−3ln(2)+ln(3)

Decimal

−0.98082…

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Solution steps

One step at a time

L⁻¹{x²−25x²+4x−5 }

以下の部分分数を得る: x²−25x²+4x−5 : 1−4x−1

=L⁻¹{1−4x−1 }

逆ラプラス変換の線形性を使用する:
関数 f(s), g(s) と定数 a, b: L⁻¹{a·f(s)+b·g(s)}=a·L⁻¹{f(s)}+b·L⁻¹{g(s)}

=L⁻¹{1}−L⁻¹{4x−1 }

L⁻¹{1}: δ(t)

L⁻¹{4x−1 }: 4e^t

=δ(t)−4e^t

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こんにちは, について質問する部分分数 ∫₀¹x−4x²−5x+6 dx または以下を選択してください

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

d/(dt)(sin^2(t))

Solution

Solution steps

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