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integral of arctan(-x)

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

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∫ arctan(−x)dx

Solution

xarctan(−x)+12 ln|x²+1|+C

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∫ arctan(−x)dx

Apply Integration By Parts: xarctan(−x)−∫ −xx²+1 dx

=xarctan(−x)−∫ −xx²+1 dx

∫ −xx²+1 dx=−12 ln|x²+1|

=xarctan(−x)−(−12 ln|x²+1|)

Simplify

=xarctan(−x)+12 ln|x²+1|

Add a constant to the solution

=xarctan(−x)+12 ln|x²+1|+C

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

integral of arctan(-x)

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