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inversa (5x-x^2)/(x^4-25x^2)

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

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transformadora de laplace cos³(t)

Solution

s4(s²+9) +3s4(s²+1)

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Solution steps

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∫ sin²(x)cos³(x)dx

Reeecreva usando identidades trigonométricas

=∫ (1−sin²(x))cos(x)sin²(x)dx

Aplicar integração por substituição: ∫ u²(1−u²)du

=∫ u²(1−u²)du

Expandir u²(1−u²): u²−u⁴

=∫ u²−u⁴du

Aplicar a regra da soma: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=∫ u²du−∫ u⁴du

∫ u²du=u³3

∫ u⁴du=u⁵5

=u³3 −u⁵5

Substituir na equação u=sin(x)

=sin³(x)3 −sin⁵(x)5

Adicionar uma constante à solução

=sin³(x)3 −sin⁵(x)5 +C

Verify Result

=sin³(x)3 −sin⁵(x)5 +C

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inversa de laplace cos³(t)

Order of operations three/four steps with parentheses Examples

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

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inversa (5x-x^2)/(x^4-25x^2)

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inversa (5x-x^2)/(x^4-25x^2)

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