What is the integral of-3|x| ?

The integral of-3|x| is -3/2 x|x|+C

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integral of-3|x|

\int - 3 ∣ x ∣ d x

- \frac{3}{2} x ∣ x ∣ + C

Solution steps

\int - 3 ∣ x ∣ d x

Take the constant out:

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

= - 3 \cdot \int ∣ x ∣ d x

Use the common integral:

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

= - 3 \cdot \frac{x ∣ x ∣}{2}

Simplify

- 3 \cdot \frac{x ∣ x ∣}{2} : - \frac{3}{2} x ∣ x ∣

= - \frac{3}{2} x ∣ x ∣

Add a constant to the solution

= - \frac{3}{2} x ∣ x ∣ + C

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\int \frac{x + 1 + 1}{x + 1 - 1} d x

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

\int \frac{- x}{1 - x} d x