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linear 4xy^{\prime \prime}+2y^{\prime}+y=0

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

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

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∫ sin⁷(x)cos⁶(x)dx

Solution

−cos⁷(x)7 +cos⁹(x)3 −3cos¹¹(x)11 +cos¹³(x)13 +C

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∫ sin⁷(x)cos⁶(x)dx

Reeecreva usando identidades trigonométricas

=∫ (1−cos²(x))³sin(x)cos⁶(x)dx

Aplicar integração por substituição: ∫ −u⁶(1−u²)³du

=∫ −u⁶(1−u²)³du

Expandir −u⁶(1−u²)³: −u⁶+3u⁸−3u¹⁰+u¹²

=∫ −u⁶+3u⁸−3u¹⁰+u¹²du

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

=−∫ u⁶du+∫ 3u⁸du−∫ 3u¹⁰du+∫ u¹²du

∫ u⁶du=u⁷7

∫ 3u⁸du=u⁹3

∫ 3u¹⁰du=3u¹¹11

∫ u¹²du=u¹³13

=−u⁷7 +u⁹3 −3u¹¹11 +u¹³13

Substituir na equação u=cos(x)

=−cos⁷(x)7 +cos⁹(x)3 −3cos¹¹(x)11 +cos¹³(x)13

Adicionar uma constante à solução

=−cos⁷(x)7 +cos⁹(x)3 −3cos¹¹(x)11 +cos¹³(x)13 +C

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

linear 4xy^{\prime \prime}+2y^{\prime}+y=0

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linear 4xy^{\prime \prime}+2y^{\prime}+y=0

Solution

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