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range of sin^2(x)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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∫ sin⁴(x)cos³(x)dx

Solution

sin⁵(x)5 −sin⁷(x)7 +C

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∫ sin⁴(x)cos³(x)dx

三角関数の公式を使用して書き換える

=∫ (1−sin²(x))cos(x)sin⁴(x)dx

u置換積分法を適用する: ∫ u⁴(1−u²)du

=∫ u⁴(1−u²)du

拡張 u⁴(1−u²): u⁴−u⁶

=∫ u⁴−u⁶du

総和規則を適用する: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=∫ u⁴du−∫ u⁶du

∫ u⁴du=u⁵5

∫ u⁶du=u⁷7

=u⁵5 −u⁷7

代用を戻す u=sin(x)

=sin⁵(x)5 −sin⁷(x)7

定数を解答に追加する

=sin⁵(x)5 −sin⁷(x)7 +C

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こんにちは, について質問する ∫ sin⁴(x)cos³(x)dx または以下のオプションから選択してください

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

range of sin^2(x)

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range of sin^2(x)

Solution

Solution steps

Number Line

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