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

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

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

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

\frac{3 x ^{2}}{2} - 5 x + C

Solution steps

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

Expand

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

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

\int \frac{5 x}{x} d x = 5 x

= \frac{3 x ^{2}}{2} - 5 x

Add a constant to the solution

= \frac{3 x ^{2}}{2} - 5 x + C

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