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simetria x²−3x−4

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x=32

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∫ cos⁷(x)sin⁴(x)dx

Rewrite using trig identities

=∫ (1−sin²(x))³cos(x)sin⁴(x)dx

Apply u-substitution: ∫ u⁴(1−u²)³du

=∫ u⁴(1−u²)³du

Expand u⁴(1−u²)³: u⁴−3u⁶+3u⁸−u¹⁰

=∫ u⁴−3u⁶+3u⁸−u¹⁰du

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

=∫ u⁴du−∫ 3u⁶du+∫ 3u⁸du−∫ u¹⁰du

∫ u⁴du=u⁵5

∫ 3u⁶du=3u⁷7

∫ 3u⁸du=u⁹3

∫ u¹⁰du=u¹¹11

=u⁵5 −3u⁷7 +u⁹3 −u¹¹11

Substitute back u=sin(x)

=sin⁵(x)5 −3sin⁷(x)7 +sin⁹(x)3 −sin¹¹(x)11

Add a constant to the solution

=sin⁵(x)5 −3sin⁷(x)7 +sin⁹(x)3 −sin¹¹(x)11 +C

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

next term a_{n}=3^{n-1}

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next term a_{n}=3^{n-1}

Solution

Solution steps

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