tính tuần hoàn cos^{855}(x)

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

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∫

ddx

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

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∫ xsin²(x)cot²(x)cos⁴(x) dx

Solution

xtan(x)+ln|cos(x)|+C

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∫ xsin²(x)cot²(x)cos⁴(x) dx

Viết lại bằng cách sử dụng hằng đẳng thức lượng giác

=∫ 2x1+cos(2x) dx

Đưa hằng số ra ngoài: ∫a·f(x)dx=a·∫f(x)dx

=2· ∫ x1+cos(2x) dx

Áp dụng tích phân từng phần: 12 xtan(x)−∫ 12 tan(x)dx

=2(12 xtan(x)−∫ 12 tan(x)dx)

∫ 12 tan(x)dx=−12 ln|cos(x)|

=2(12 xtan(x)−(−12 ln|cos(x)|))

Rút gọn 2(12 xtan(x)−(−12 ln|cos(x)|)): xtan(x)+ln|cos(x)|

=xtan(x)+ln|cos(x)|

Thêm một hằng số vào Lời giải

=xtan(x)+ln|cos(x)|+C

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

tính tuần hoàn cos^{855}(x)

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