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Popular Calculus >

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

Solution

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

Solution

x^{2} - x + C

Solution steps

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

Expand

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

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

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

= x^{2} - x

Add a constant to the solution

= x^{2} - x + C

Graph

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Frequently Asked Questions (FAQ)

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