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обратная 9x^2

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

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(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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интеграл e^−xcos(x)

Solution

e^−xsin(x)2 −e^−xcos(x)2 +C

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∫ e^−xcos(x)dx

Применить интегрирование по частям: e^−xsin(x)−∫ −e^−xsin(x)dx

=e^−xsin(x)−∫ −e^−xsin(x)dx

Извлечь константу: ∫a·f(x)dx=a·∫f(x)dx

=e^−xsin(x)−(−∫ e^−xsin(x)dx)

Применить интегрирование по частям: −e^−xcos(x)−∫ e^−xcos(x)dx

=e^−xsin(x)−(−(−e^−xcos(x)−∫ e^−xcos(x)dx))

Поэтому

∫ e^−xcos(x)dx=e^−xsin(x)−(−(−e^−xcos(x)−∫ e^−xcos(x)dx))

Отделять ∫ e^−xcos(x)dx

=e^−xsin(x)2 −e^−xcos(x)2

Добавить константу к решению

=e^−xsin(x)2 −e^−xcos(x)2 +C

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

обратная 9x^2

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