What is the integral of (5x^2+7x-11)/(x^2) ?

The integral of (5x^2+7x-11)/(x^2) is 5x+7ln|x|+(11)/x+C

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integral of (5x^2+7x-11)/(x^2)

\int \frac{5 x ^{2} + 7 x - 11}{x ^{2}} d x

5 x + 7 ln ∣ x ∣ + \frac{11}{x} + C

Solution steps

\int \frac{5 x ^{2} + 7 x - 11}{x ^{2}} d x

Expand

\frac{5 x ^{2} + 7 x - 11}{x ^{2}} : 5 + \frac{7}{x} - \frac{11}{x ^{2}}

= \int 5 + \frac{7}{x} - \frac{11}{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 5 d x + \int \frac{7}{x} d x - \int \frac{11}{x ^{2}} d x

\int 5 d x = 5 x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

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

= 5 x + 7 ln ∣ x ∣ - (- \frac{11}{x})

Simplify

= 5 x + 7 ln ∣ x ∣ + \frac{11}{x}

Add a constant to the solution

= 5 x + 7 ln ∣ x ∣ + \frac{11}{x} + C

\int (2 x + 6) e^{- 4 x} d x

\frac{\partial}{\partial x} (cos (5 x))

f (x) = (8 x + 9) (9 x - 10)

\frac{d}{d x} (7 (cos (x^{2}) - 2 x^{2} sin (x^{2})))

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

What is the integral of (5x^2+7x-11)/(x^2) ?
The integral of (5x^2+7x-11)/(x^2) is 5x+7ln|x|+(11)/x+C