What is the integral of (x^2-4x-6)/(x^2-6x) ?

The integral of (x^2-4x-6)/(x^2-6x) is ln|x^2-6x|+x+C

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integral of (x^2-4x-6)/(x^2-6x)

\int \frac{x ^{2} - 4 x - 6}{x ^{2} - 6 x} d x

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

Solution steps

\int \frac{x ^{2} - 4 x - 6}{x ^{2} - 6 x} d x

\frac{x ^{2} - 4 x - 6}{x ^{2} - 6 x} = \frac{2 x - 6}{x ^{2} - 6 x} + 1

= \int \frac{2 x - 6}{x ^{2} - 6 x} + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2 x - 6}{x ^{2} - 6 x} d x + \int 1 d x

\int \frac{2 x - 6}{x ^{2} - 6 x} d x = ln x^{2} - 6 x

\int 1 d x = x

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

Add a constant to the solution

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

\int_{3}^{7} \frac{x}{7 + x ^{2}} d x

\frac{d}{d x} (\frac{x ln ( x )}{e ^{x}})

\frac{\partial}{\partial x} (x^{\frac{1}{3}} y^{\frac{1}{3}})

\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{x}{2}) - tan (\frac{x}{2}))

\frac{d}{d x} (sec^{4} (2) x^{2})

What is the integral of (x^2-4x-6)/(x^2-6x) ?
The integral of (x^2-4x-6)/(x^2-6x) is ln|x^2-6x|+x+C