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_{2}^{3} π (x + x^{2})^{2} d x

f (x) = \frac{11}{2} - x^{2}, at x = - 2

\int cos (2 x - 3) d x

k = 0 \sum \infty (\frac{1}{2})^{2 k + 1}

\frac{x ( x - 1 ) ( x - 2 ) ( x - 3 )}{24}

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