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

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

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integral of-(x^2)/x

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Cancel the common factor:

x

= - \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

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

Add a constant to the solution

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

\frac{1 - 5 x - x ^{2}}{x ^{2} - 3}

(e^{2 x} + 4) y^{^{'}} = y

\int (2 x + 1)^{5} d x

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 x^{2} - 5

\frac{d y}{d x} = \frac{y ^{2}}{e ^{x}}