integral of (5x^3+4)/(3x+2)

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∫ 5x³+43x+2 dx

Solution

5243 (3x+2)³−527 (3x+2)²+209 x+4027 +6881 ln|3x+2|+C

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∫ 5x³+43x+2 dx

Expand 5x³+43x+2 : 5x³3x+2 +43x+2

Apply the Sum Rule: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=∫ 5x³3x+2 dx+∫ 43x+2 dx

∫ 5x³3x+2 dx=5243 ((3x+2)³−9(3x+2)²+36(3x+2)−24ln|3x+2|)

∫ 43x+2 dx=43 ln|3x+2|

=5243 ((3x+2)³−9(3x+2)²+36(3x+2)−24ln|3x+2|)+43 ln|3x+2|

Simplify 5243 ((3x+2)³−9(3x+2)²+36(3x+2)−24ln|3x+2|)+43 ln|3x+2|: 5243 (3x+2)³−527 (3x+2)²+209 x+4027 +6881 ln|3x+2|

=5243 (3x+2)³−527 (3x+2)²+209 x+4027 +6881 ln|3x+2|

Add a constant to the solution

=5243 (3x+2)³−527 (3x+2)²+209 x+4027 +6881 ln|3x+2|+C

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

integral of (5x^3+4)/(3x+2)

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