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derivative of sqrt(4-x)

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∫ 26(x−1)(x²+25) dx

Solution

ln|x−1|−12 ln|x²+25|−15 arctan(x5 )+C

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∫ 26(x−1)(x²+25) dx

定数を除く: ∫a·f(x)dx=a·∫f(x)dx

=26· ∫ 1(x−1)(x²+25) dx

以下の部分分数を得る: 1(x−1)(x²+25) : 126(x−1) +−x−126(x²+25)

=26· ∫ 126(x−1) +−x−126(x²+25) dx

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

=26(∫ 126(x−1) dx+∫ −x−126(x²+25) dx)

∫ 126(x−1) dx=126 ln|x−1|

∫ −x−126(x²+25) dx=126 (−12 ln|x²+25|−15 arctan(x5 ))

=26(126 ln|x−1|+126 (−12 ln|x²+25|−15 arctan(x5 )))

簡素化 26(126 ln|x−1|+126 (−12 ln|x²+25|−15 arctan(x5 ))): ln|x−1|−12 ln|x²+25|−15 arctan(x5 )

=ln|x−1|−12 ln|x²+25|−15 arctan(x5 )

定数を解答に追加する

=ln|x−1|−12 ln|x²+25|−15 arctan(x5 )+C

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

derivative of sqrt(4-x)

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