What is the integral of (x^2-3x-5)/(x^2-5x) ?

The integral of (x^2-3x-5)/(x^2-5x) is ln|x^2-5x|+x+C

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integral of (x^2-3x-5)/(x^2-5x)

\int \frac{x ^{2} - 3 x - 5}{x ^{2} - 5 x} d x

ln x^{2} - 5 x + x + C

Solution steps

\int \frac{x ^{2} - 3 x - 5}{x ^{2} - 5 x} d x

\frac{x ^{2} - 3 x - 5}{x ^{2} - 5 x} = \frac{2 x - 5}{x ^{2} - 5 x} + 1

= \int \frac{2 x - 5}{x ^{2} - 5 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 - 5}{x ^{2} - 5 x} d x + \int 1 d x

\int \frac{2 x - 5}{x ^{2} - 5 x} d x = ln x^{2} - 5 x

\int 1 d x = x

= ln x^{2} - 5 x + x

Add a constant to the solution

= ln x^{2} - 5 x + x + C

y \to 0 lim (\frac{7}{y ^{2} + y} - \frac{7}{y})

5 e^{- x}

f^{^{'}} (x) = sin (x^{2})

\frac{d}{d x} ((sin (x))^{l n (x)})

\frac{\partial}{\partial x} (x^{2} y + 5 y^{3})

What is the integral of (x^2-3x-5)/(x^2-5x) ?
The integral of (x^2-3x-5)/(x^2-5x) is ln|x^2-5x|+x+C