integral of (2-sqrt(x))/(4-x)

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∫ 2−√x4−x dx

Solution

−4(12 ln|√x2 +1|−12 ln|√x2 −1|−12 √x)−2ln|x−4|+C

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Solution steps

One step at a time

tan(x)−cot(x)tan(x)+cot(x) =2sin²(x)−1

Manipulating left side

tan(x)−cot(x)tan(x)+cot(x)

Express with sin, cos

=−cos²(x)+sin²(x)cos²(x)+sin²(x)

Rewrite using trig identities

=−1+2sin²(x)

=2sin²(x)−1

We showed that the two sides could take the same form

⇒ True

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

integral of (2-sqrt(x))/(4-x)

Solution

Solution steps

Number Line

Graph

`a`	1
0	2`a`

6	−1
2	3

6	−1
2	3

6	−1
2	3