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

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

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integral of sqrt(12-4x)-x

\int 12 - 4 x - x d x

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

Solution steps

\int 12 - 4 x - x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 12 - 4 x d x - \int x d x

\int 12 - 4 x d x = - \frac{4}{3} (- x + 3)^{\frac{3}{2}}

\int x d x = \frac{x ^{2}}{2}

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

Add a constant to the solution

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

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