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foki (y-3)^2=8(x-5)

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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∫ x⁴x²+x−2 dx

Solution

x³3 −x²2 +3x+13 ln|x−1|−163 ln|x+2|+C

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∫ x⁴x²+x−2 dx

Lange Division x⁴x²+x−2 : x²−x+3+−5x+6x²+x−2

=∫ x²−x+3+−5x+6x²+x−2 dx

Wende die Summenregel an: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=∫ x²dx−∫ xdx+∫ 3dx+∫ −5x+6x²+x−2 dx

∫ x²dx=x³3

∫ xdx=x²2

∫ 3dx=3x

∫ −5x+6x²+x−2 dx=13 ln|x−1|−163 ln|x+2|

=x³3 −x²2 +3x+13 ln|x−1|−163 ln|x+2|

Füge eine Konstante zur Lösung hinzu

=x³3 −x²2 +3x+13 ln|x−1|−163 ln|x+2|+C

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

foki (y-3)^2=8(x-5)

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