What is the integral of-|x| ?

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

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integral of-|x|

\int - ∣ x ∣ d x

- \frac{x ∣ x ∣}{2} + C

Solution steps

\int - ∣ x ∣ d x

Take the constant out:

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

= - \int ∣ x ∣ d x

Use the common integral:

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= - \frac{x ∣ x ∣}{2}

Add a constant to the solution

= - \frac{x ∣ x ∣}{2} + C

\frac{d}{d x} (\frac{4 x ^{5} - 15}{x ^{4}})

y^{^{'}} = - \frac{y}{3}

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

\int \frac{x ^{2} - x + 24}{x ^{3} + 6 x} d x

y = x - 3 x^{2}, (3, - 24)