What is the integral of (2x-1)/(x^2-x-12) ?

The integral of (2x-1)/(x^2-x-12) is ln|x^2-x-12|+C

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integral of (2x-1)/(x^2-x-12)

\int \frac{2 x - 1}{x ^{2} - x - 12} d x

ln x^{2} - x - 12 + C

Solution steps

\int \frac{2 x - 1}{x ^{2} - x - 12} 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} - x - 12

= ln x^{2} - x - 12

Add a constant to the solution

= ln x^{2} - x - 12 + C

y^{^{''}} + 9 y = 5 e^{x} - 162 x

\int - \frac{x ^{3}}{3} - x^{2} + \frac{4}{3} d x

\frac{d}{d x} (2 arcsin (\frac{x}{2}))

\frac{d y}{d x} = 7 x 5 y + 11, y (0) = 9

What is the integral of (2x-1)/(x^2-x-12) ?
The integral of (2x-1)/(x^2-x-12) is ln|x^2-x-12|+C