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integral of sin(5x)

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∫ sin(5x)dx

Solution

−15 cos(5x)+C

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Solution steps

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∫ sin(5x)dx

Apply u-substitution: ∫ sin(u)15 du

=∫ sin(u)15 du

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

=15 · ∫ sin(u)du

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

=15 (−cos(u))

Substitute back u=5x

=15 (−cos(5x))

Simplify

=−15 cos(5x)

Add a constant to the solution

=−15 cos(5x)+C

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

integral of sin(5x)

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