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Integrate (4x-6)/2x^2-6x

Videos

$\frac{1}{128}\left(64\left(x-\frac{3}{2}\right)^{4}+4\left(4x-6\right)\left(16x^2-48x+36\right)+18\left(16x^2-48x+36\right)\right)-3x^2+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(\frac{4x-6}{2} x^2-6x\right)dx$
1

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int x^2\frac{4x-6}{2}dx+\int-6xdx$
2

Take the constant out of the integral

$\int x^2\frac{4x-6}{2}dx-6\int xdx$

$\frac{1}{128}\left(64\left(x-\frac{3}{2}\right)^{4}+4\left(4x-6\right)\left(16x^2-48x+36\right)+18\left(16x^2-48x+36\right)\right)-3x^2+C_0$
$\int\left(\frac{4x-6}{2} x^2-6x\right)dx$

Main topic:

Integration by substitution

~ 3.76 seconds