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negative reciprocal of x^2

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∫ (x³−21x)(5+4x−x²) dx

Solution

−x²2 −4x+20(16 ln|x+1|−16 ln|x−5|)+C

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∫ x³−21x5+4x−x² dx

Divisão longa x³−21x5+4x−x² : −x−4+20−x²+4x+5

=∫ −x−4+20−x²+4x+5 dx

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

=−∫ xdx−∫ 4dx+∫ 20−x²+4x+5 dx

∫ xdx=x²2

∫ 4dx=4x

∫ 20−x²+4x+5 dx=20(16 ln|x+1|−16 ln|x−5|)

=−x²2 −4x+20(16 ln|x+1|−16 ln|x−5|)

Adicionar uma constante à solução

=−x²2 −4x+20(16 ln|x+1|−16 ln|x−5|)+C

Function Negative Reciprocal Examples

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

negative reciprocal of x^2

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