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

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

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

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

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

Solution steps

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

Simplify

\frac{x ^{3} - x ^{2}}{x ^{2}} : x - 1

= \int x - 1 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 x d x - \int 1 d x

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

\int 1 d x = x

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

Add a constant to the solution

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

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

\int e^{4 x} d x

\int (csc (5 x))^{3} d x

f (x) = ln (x + 2)

\frac{d}{d x} (sin (\frac{5 x - 3 x ^{3}}{x + 1}))

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