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laplace transform sin(x)

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∫ (x−6)(5x²−6x+8) dx

Solution

110 ln|25x²−30x+40|−275√31 arctan(1√31 (5x−3))+C

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∫ x−65x²−6x+8 dx

Expand x−65x²−6x+8 : x5x²−6x+8 −65x²−6x+8

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

=∫ x5x²−6x+8 dx−∫ 65x²−6x+8 dx

∫ x5x²−6x+8 dx=110 ln|25x²−30x+40|+35√31 arctan(5x−3√31 )

∫ 65x²−6x+8 dx=6√31 arctan(5x−3√31 )

=110 ln|25x²−30x+40|+35√31 arctan(5x−3√31 )−6√31 arctan(5x−3√31 )

Simplify 110 ln|25x²−30x+40|+35√31 arctan(5x−3√31 )−6√31 arctan(5x−3√31 ): 110 ln|25x²−30x+40|−275√31 arctan(1√31 (5x−3))

=110 ln|25x²−30x+40|−275√31 arctan(1√31 (5x−3))

Add a constant to the solution

=110 ln|25x²−30x+40|−275√31 arctan(1√31 (5x−3))+C

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

laplace transform sin(x)

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