integral of sin(x-7)

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∫ sin(x−7)dx

Solution

xsin(x−7)+xsin(7−x)−cos(7−x)+C

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∫ sin(x−7)dx

Apply Integration By Parts: sin(x−7)x−∫ cos(x−7)xdx

=sin(x−7)x−∫ cos(x−7)xdx

∫ cos(x−7)xdx=−xsin(7−x)+cos(7−x)

=sin(x−7)x−(−xsin(7−x)+cos(7−x))

Simplify sin(x−7)x−(−xsin(7−x)+cos(7−x)): xsin(x−7)+xsin(7−x)−cos(7−x)

=xsin(x−7)+xsin(7−x)−cos(7−x)

Add a constant to the solution

=xsin(x−7)+xsin(7−x)−cos(7−x)+C

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

integral of sin(x-7)

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