What is the integral of (sqrt(8x-2x)) ?

The integral of (sqrt(8x-2x)) is (2sqrt(2))/(sqrt(3))x^{3/2}+C

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integral of (sqrt(8x-2x))

\int (8 x - 2 x) d x

\frac{2 2}{3} x^{\frac{3}{2}} + C

Solution steps

\int 8 x - 2 x d x

Simplify

8 x - 2 x : 6 x

= \int 6 x d x

Take the constant out:

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

= 6 \cdot \int x d x

Apply the Power Rule

= 6 \frac{2}{3} x^{\frac{3}{2}}

Simplify

6 \frac{2}{3} x^{\frac{3}{2}} : \frac{2 2}{3} x^{\frac{3}{2}}

= \frac{2 2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{2 2}{3} x^{\frac{3}{2}} + C

What is the integral of (sqrt(8x-2x)) ?
The integral of (sqrt(8x-2x)) is (2sqrt(2))/(sqrt(3))x^{3/2}+C