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

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

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

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

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

Solution steps

\int \frac{2 x - 3}{x ^{2} - 3 x + 6} 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 = x^{2} - 3 x + 6

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

Add a constant to the solution

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

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