What is the integral of 20-3sqrt(16-2x) ?

The integral of 20-3sqrt(16-2x) is 20x+(16-2x)^{3/2}+C

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integral of 20-3sqrt(16-2x)

\int 20 - 3 16 - 2 x d x

20 x + (16 - 2 x)^{\frac{3}{2}} + C

Solution steps

\int 20 - 3 16 - 2 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 20 d x - \int 3 16 - 2 x d x

\int 20 d x = 20 x

\int 3 16 - 2 x d x = - (16 - 2 x)^{\frac{3}{2}}

= 20 x - (- (16 - 2 x)^{\frac{3}{2}})

Simplify

= 20 x + (16 - 2 x)^{\frac{3}{2}}

Add a constant to the solution

= 20 x + (16 - 2 x)^{\frac{3}{2}} + C

y = 3 x, y = x^{2}

e^{x} ln (1 + x)

x \to 4 lim (\frac{3 - x}{x - 4})

\frac{1}{( s + 1 ) ( s + 2 )}

x \to 0 lim (2 x + c)

What is the integral of 20-3sqrt(16-2x) ?
The integral of 20-3sqrt(16-2x) is 20x+(16-2x)^{3/2}+C