integral of ((4x^2-13x-5))/((x-2))

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∫ (4x²−13x−5)(x−2) dx

Solution

2x²−5x−15ln|x−2|+2+C

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∫ 4x²−13x−5x−2 dx

Expand 4x²−13x−5x−2 : 4x²x−2 −13xx−2 −5x−2

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

=∫ 4x²x−2 dx−∫ 13xx−2 dx−∫ 5x−2 dx

∫ 4x²x−2 dx=4((x−2)²2 +4(x−2)+4ln|x−2|)

∫ 13xx−2 dx=13(x−2+2ln|x−2|)

∫ 5x−2 dx=5ln|x−2|

=4((x−2)²2 +4(x−2)+4ln|x−2|)−13(x−2+2ln|x−2|)−5ln|x−2|

Simplify 4((x−2)²2 +4(x−2)+4ln|x−2|)−13(x−2+2ln|x−2|)−5ln|x−2|: 2x²−5x−15ln|x−2|+2

=2x²−5x−15ln|x−2|+2

Add a constant to the solution

=2x²−5x−15ln|x−2|+2+C

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integral of ((4x^2-13x-5))/((x-2))

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