What is the integral of (-x^2+11x-18)/(x^2) ?

The integral of (-x^2+11x-18)/(x^2) is -x+11ln|x|+(18)/x+C

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integral of (-x^2+11x-18)/(x^2)

\int \frac{- x ^{2} + 11 x - 18}{x ^{2}} d x

- x + 11 ln ∣ x ∣ + \frac{18}{x} + C

Solution steps

\int \frac{- x ^{2} + 11 x - 18}{x ^{2}} d x

Expand

\frac{- x ^{2} + 11 x - 18}{x ^{2}} : - 1 + \frac{11}{x} - \frac{18}{x ^{2}}

= \int - 1 + \frac{11}{x} - \frac{18}{x ^{2}} 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 1 d x + \int \frac{11}{x} d x - \int \frac{18}{x ^{2}} d x

\int 1 d x = x

\int \frac{11}{x} d x = 11 ln ∣ x ∣

\int \frac{18}{x ^{2}} d x = - \frac{18}{x}

= - x + 11 ln ∣ x ∣ - (- \frac{18}{x})

Simplify

= - x + 11 ln ∣ x ∣ + \frac{18}{x}

Add a constant to the solution

= - x + 11 ln ∣ x ∣ + \frac{18}{x} + C

\int x^{\frac{5}{7}} d x

\int 3 cos^{3} (4 x) d x

\int x^{4} e^{(x^{5} - 2)} d x

x y^{^{'}} + 3 y = 8 x^{2} - 6 x

\frac{d}{d x} (\frac{( x + 1 ) ^{2}}{1 + x ^{2}})

What is the integral of (-x^2+11x-18)/(x^2) ?
The integral of (-x^2+11x-18)/(x^2) is -x+11ln|x|+(18)/x+C