What is the integral of 3/x+10x-3 ?

The integral of 3/x+10x-3 is 3ln|x|+5x^2-3x+C

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integral of 3/x+10x-3

\int \frac{3}{x} + 10 x - 3 d x

3 ln ∣ x ∣ + 5 x^{2} - 3 x + C

Solution steps

\int \frac{3}{x} + 10 x - 3 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 \frac{3}{x} d x + \int 10 x d x - \int 3 d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 10 x d x = 5 x^{2}

\int 3 d x = 3 x

= 3 ln ∣ x ∣ + 5 x^{2} - 3 x

Add a constant to the solution

= 3 ln ∣ x ∣ + 5 x^{2} - 3 x + C

\int_{1}^{2} \frac{7 ln ( x )}{x ^{2}} d x

\frac{\partial}{\partial x} (\frac{1}{1 - b x})

\int \frac{arctan ( 5 x )}{1 + 25 x ^{2}} d x

\frac{d}{d x} ((2 x - 7)^{4} (x^{2} + x + 1)^{5})

What is the integral of 3/x+10x-3 ?
The integral of 3/x+10x-3 is 3ln|x|+5x^2-3x+C