What is the probability of rolling 2 standard dice which sum to 11

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

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

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∫ x³x²−5x+6 dx

Solution

x²2 +5x−8ln|x−2|+27ln|x−3|+C

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Solution steps

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∫ x³x²−5x+6 dx

Long division x³x²−5x+6 : x+5+19x−30x²−5x+6

=∫ x+5+19x−30x²−5x+6 dx

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

=∫ xdx+∫ 5dx+∫ 19x−30x²−5x+6 dx

∫ xdx=x²2

∫ 5dx=5x

∫ 19x−30x²−5x+6 dx=−8ln|x−2|+27ln|x−3|

=x²2 +5x−8ln|x−2|+27ln|x−3|

Add a constant to the solution

=x²2 +5x−8ln|x−2|+27ln|x−3|+C

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
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What is the probability of rolling 2 standard dice which sum to 11

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