integral of (x^3-4x-10)/(x^2-x-6)

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

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∫ x³−4x−10x²−x−6 dx

Solution

x²2 +x+2ln|x+2|+ln|x−3|+C

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∫ x³−4x−10x²−x−6 dx

Take the partial fraction of x³−4x−10x²−x−6 : x+1+2x+2 +1x−3

=∫ x+1+2x+2 +1x−3 dx

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

=∫ xdx+∫ 1dx+∫ 2x+2 dx+∫ 1x−3 dx

∫ xdx=x²2

∫ 1dx=x

∫ 2x+2 dx=2ln|x+2|

∫ 1x−3 dx=ln|x−3|

=x²2 +x+2ln|x+2|+ln|x−3|

Add a constant to the solution

=x²2 +x+2ln|x+2|+ln|x−3|+C

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

integral of (x^3-4x-10)/(x^2-x-6)

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