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

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

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integral of ((3x^2-x+2e))/(x^2)

\int \frac{( 3 x ^{2} - x + 2 e )}{x ^{2}} d x

3 x - ln ∣ x ∣ - \frac{2 e}{x} + C

Solution steps

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

Expand

\frac{3 x ^{2} - x + 2 e}{x ^{2}} : 3 - \frac{1}{x} + \frac{2 e}{x ^{2}}

= \int 3 - \frac{1}{x} + \frac{2 e}{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 3 d x - \int \frac{1}{x} d x + \int \frac{2 e}{x ^{2}} d x

\int 3 d x = 3 x

\int \frac{1}{x} d x = ln ∣ x ∣

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

= 3 x - ln ∣ x ∣ - \frac{2 e}{x}

Add a constant to the solution

= 3 x - ln ∣ x ∣ - \frac{2 e}{x} + C

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

\frac{d}{d y} (2 y)

x \to 3 - lim (\frac{∣ 3 - x ∣}{3 - x})

\int \frac{1}{( 3 + x ^{2} ) ^{\frac{3}{2}}} d x

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

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