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amplitude of 1-sec^2(x)

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

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log_□

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ddx

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

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∫ sin³(x)cos⁸(x)dx

Solution

−cos⁹(x)9 +cos¹¹(x)11 +C

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Solution steps

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∫ sin³(x)cos⁸(x)dx

Reeecreva usando identidades trigonométricas

=∫ (1−cos²(x))sin(x)cos⁸(x)dx

Aplicar integração por substituição: ∫ −u⁸(1−u²)du

=∫ −u⁸(1−u²)du

Expandir −u⁸(1−u²): −u⁸+u¹⁰

=∫ −u⁸+u¹⁰du

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

=−∫ u⁸du+∫ u¹⁰du

∫ u⁸du=u⁹9

∫ u¹⁰du=u¹¹11

=−u⁹9 +u¹¹11

Substituir na equação u=cos(x)

=−cos⁹(x)9 +cos¹¹(x)11

Adicionar uma constante à solução

=−cos⁹(x)9 +cos¹¹(x)11 +C

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

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amplitude of 1-sec^2(x)

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