integral of 2xcos(x)

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

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∫ 2xcos(x)dx

Solution

2(xsin(x)+cos(x))+C

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∫ 2xcos(x)dx

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

=2· ∫ xcos(x)dx

Apply Integration By Parts: xsin(x)−∫ sin(x)dx

=2(xsin(x)−∫ sin(x)dx)

∫ sin(x)dx=−cos(x)

=2(xsin(x)−(−cos(x)))

Simplify

=2(xsin(x)+cos(x))

Add a constant to the solution

=2(xsin(x)+cos(x))+C

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

integral of 2xcos(x)

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