gamme x^3

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

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∫ x³−5(x−3)² dx

Solution

x²2 +6x+27ln|x−3|−22x−3 +C

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∫ x³−5(x−3)² dx

Long division x³−5(x−3)² : x+6+27x−59x²−6x+9

=∫ x+6+27x−59x²−6x+9 dx

Apply the Sum Rule: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=∫ xdx+∫ 6dx+∫ 27x−59x²−6x+9 dx

∫ xdx=x²2

∫ 6dx=6x

∫ 27x−59x²−6x+9 dx=27ln|x−3|−22x−3

=x²2 +6x+27ln|x−3|−22x−3

Add a constant to the solution

=x²2 +6x+27ln|x−3|−22x−3 +C

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

gamme x^3

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