What is the integral of |x+2| ?

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

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integral of |x+2|

\int ∣ x + 2 ∣ d x

\frac{( x + 2 ) ∣ x + 2 ∣}{2} + C

Solution steps

\int ∣ x + 2 ∣ d x

Apply u-substitution

: \int ∣ u ∣ d u

= \int ∣ u ∣ d u

Use the common integral:

\int ∣ u ∣ d u = \frac{u ∣ u ∣}{2}

= \frac{u ∣ u ∣}{2}

Substitute back

u = x + 2

= \frac{( x + 2 ) ∣ x + 2 ∣}{2}

Add a constant to the solution

= \frac{( x + 2 ) ∣ x + 2 ∣}{2} + C

\frac{d}{d x} ((5 x^{2} - 3) \cdot (x^{2} + x + 4))

\frac{d}{d x} (e^{x} (12 x^{2} - 24 x + 24))

\int \frac{4 x - 3}{2 x ^{2} - 3 x - 14} d x

y^{^{'''}} + 8 y^{^{''}} + 5 y^{^{'}} - 50 y = 0

(\frac{x + 2}{x - 2})^{2}