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

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

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

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

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

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