What is the integral of ((3x-7x^2)/x) ?

The integral of ((3x-7x^2)/x) is 3x-(7x^2)/2+C

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integral of ((3x-7x^2)/x)

\int (\frac{3 x - 7 x ^{2}}{x}) d x

3 x - \frac{7 x ^{2}}{2} + C

Solution steps

\int \frac{3 x - 7 x ^{2}}{x} d x

Expand

\frac{3 x - 7 x ^{2}}{x} : \frac{3 x}{x} - \frac{7 x ^{2}}{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}{x} d x - \int \frac{7 x ^{2}}{x} d x

\int \frac{3 x}{x} d x = 3 x

\int \frac{7 x ^{2}}{x} d x = \frac{7 x ^{2}}{2}

= 3 x - \frac{7 x ^{2}}{2}

Add a constant to the solution

= 3 x - \frac{7 x ^{2}}{2} + C

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What is the integral of ((3x-7x^2)/x) ?
The integral of ((3x-7x^2)/x) is 3x-(7x^2)/2+C