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integral of cos^2(x)

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∫ 5x³+1x²−4 dx

Solution

52 (x²−4+4ln|x²−4|)−14 (ln|x2 +1|−ln|x2 −1|)+C

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∫ 5x³+1x²−4 dx

Расширить 5x³+1x²−4 : 5x³x²−4 +1x²−4

Применить правило суммы: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=∫ 5x³x²−4 dx+∫ 1x²−4 dx

∫ 5x³x²−4 dx=52 (x²−4+4ln|x²−4|)

∫ 1x²−4 dx=−14 (ln|x2 +1|−ln|x2 −1|)

=52 (x²−4+4ln|x²−4|)−14 (ln|x2 +1|−ln|x2 −1|)

Добавить константу к решению

=52 (x²−4+4ln|x²−4|)−14 (ln|x2 +1|−ln|x2 −1|)+C

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

integral of cos^2(x)

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