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integral of x/((x^2+1)^2)

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∫ x(x²+1)² dx

Solution

−12(x²+1) +C

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∫ x(x²+1)² dx

Apply u-substitution: ∫ 12u² du

=∫ 12u² du

Take the constant out: ∫a·f(x)dx=a·∫f(x)dx

=12 · ∫ 1u² du

Apply the Power Rule: −1u

=12 (−1u )

Substitute back u=x²+1

=12 (−1x²+1 )

Simplify 12 (−1x²+1 ): −12(x²+1)

=−12(x²+1)

Add a constant to the solution

=−12(x²+1) +C

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

integral of x/((x^2+1)^2)

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