x/(x-5)+2= 2/(x-5)

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

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simplify solve for inverse tangent line

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∫ sin(2x+5)dx

Solution

−12 cos(2x+5)+C

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Solution steps

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∫ sin(2x+5)dx

Apply u-substitution: ∫ sin(u)12 du

=∫ sin(u)12 du

Take the constant out: ∫a·f(x)dx=a·∫f(x)dx

=12 · ∫ sin(u)du

Use the common integral: ∫ sin(u)du=−cos(u)

=12 (−cos(u))

Substitute back u=2x+5

=12 (−cos(2x+5))

Simplify

=−12 cos(2x+5)

Add a constant to the solution

=−12 cos(2x+5)+C

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

x/(x-5)+2= 2/(x-5)

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