integral of xcos^2x

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

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∫ xcos²(x)dx

Solution

12 x(x+12 sin(2x))−12 (x²2 −14 cos(2x))+C

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∫ xcos²(x)dx

Apply Integration By Parts: 12 x(x+12 sin(2x))−∫ 12 (x+12 sin(2x))dx

=12 x(x+12 sin(2x))−∫ 12 (x+12 sin(2x))dx

∫ 12 (x+12 sin(2x))dx=12 (x²2 −14 cos(2x))

=12 x(x+12 sin(2x))−12 (x²2 −14 cos(2x))

Add a constant to the solution

=12 x(x+12 sin(2x))−12 (x²2 −14 cos(2x))+C

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

integral of xcos^2x

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