What is the integral of sqrt(12-4x) ?

The integral of sqrt(12-4x) is -4/3 (-x+3)^{3/2}+C

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integral of sqrt(12-4x)

\int 12 - 4 x d x

- \frac{4}{3} (- x + 3)^{\frac{3}{2}} + C

Solution steps

\int 12 - 4 x d x

Apply u-substitution

= \int - \frac{u}{4} d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int u d u

Apply the Power Rule

= - \frac{1}{4} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 12 - 4 x

= - \frac{1}{4} \cdot \frac{2}{3} (12 - 4 x)^{\frac{3}{2}}

Simplify

- \frac{1}{4} \cdot \frac{2}{3} (12 - 4 x)^{\frac{3}{2}} : - \frac{4}{3} (- x + 3)^{\frac{3}{2}}

= - \frac{4}{3} (- x + 3)^{\frac{3}{2}}

Add a constant to the solution

= - \frac{4}{3} (- x + 3)^{\frac{3}{2}} + C

What is the integral of sqrt(12-4x) ?
The integral of sqrt(12-4x) is -4/3 (-x+3)^{3/2}+C