What is the integral of ((6-6x))/((6x-3x^2)) ?

The integral of ((6-6x))/((6x-3x^2)) is ln|6x-3x^2|+C

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integral of ((6-6x))/((6x-3x^2))

\int \frac{( 6 - 6 x )}{( 6 x - 3 x ^{2} )} d x

ln 6 x - 3 x^{2} + C

Solution steps

\int \frac{6 - 6 x}{6 x - 3 x ^{2}} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 6 x - 3 x^{2}

= ln 6 x - 3 x^{2}

Add a constant to the solution

= ln 6 x - 3 x^{2} + C

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What is the integral of ((6-6x))/((6x-3x^2)) ?
The integral of ((6-6x))/((6x-3x^2)) is ln|6x-3x^2|+C