What is the integral of (6x^2-5x+3)/x ?

The integral of (6x^2-5x+3)/x is 3x^2-5x+3ln|x|+C

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integral of (6x^2-5x+3)/x

\int \frac{6 x ^{2} - 5 x + 3}{x} d x

3 x^{2} - 5 x + 3 ln ∣ x ∣ + C

Solution steps

\int \frac{6 x ^{2} - 5 x + 3}{x} d x

Expand

\frac{6 x ^{2} - 5 x + 3}{x} : 6 x - 5 + \frac{3}{x}

= \int 6 x - 5 + \frac{3}{x} 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 6 x d x - \int 5 d x + \int \frac{3}{x} d x

\int 6 x d x = 3 x^{2}

\int 5 d x = 5 x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= 3 x^{2} - 5 x + 3 ln ∣ x ∣

Add a constant to the solution

= 3 x^{2} - 5 x + 3 ln ∣ x ∣ + C

\frac{\partial}{\partial x} (3 x y e^{y - x})

(3, 3), (2, - 5)

(x^{2} - 5) y y^{^{'}} = 2 x

\int \frac{x}{3} \cdot sin (x^{2}) d x

\int (x) d x

What is the integral of (6x^2-5x+3)/x ?
The integral of (6x^2-5x+3)/x is 3x^2-5x+3ln|x|+C