What is the integral of |x-3| ?

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

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integral of |x-3|

\int ∣ x - 3 ∣ d x

\frac{( x - 3 ) ∣ x - 3 ∣}{2} + C

Solution steps

\int ∣ x - 3 ∣ 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 - 3

= \frac{( x - 3 ) ∣ x - 3 ∣}{2}

Add a constant to the solution

= \frac{( x - 3 ) ∣ x - 3 ∣}{2} + C

f (x) = (\frac{x + 2}{x - 2})^{5}

f (x) = x^{2} 1 - x^{2}

\frac{\partial}{\partial x} (3 x e^{x^{2} + y^{2}})

\int \frac{cos ( x )}{sin ^{2} ( x ) - 49} d x

\frac{d}{d x} (tan^{2} (x^{2} - 5 x))