integral of sin^2(x)cos^2(x)

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∫ sin²(x)cos²(x)dx

Solution

18 (x−14 sin(4x))+C

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∫ sin²(x)cos²(x)dx

Rewrite using trig identities

=∫ 1−cos(4x)8 dx

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

=18 · ∫ 1−cos(4x)dx

Apply the Sum Rule: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=18 (∫ 1dx−∫ cos(4x)dx)

∫ 1dx=x

∫ cos(4x)dx=14 sin(4x)

=18 (x−14 sin(4x))

Add a constant to the solution

=18 (x−14 sin(4x))+C

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

integral of sin^2(x)cos^2(x)

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