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

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

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integral of 2sqrt(8x)

\int 2 8 x d x

\frac{8 2}{3} x^{\frac{3}{2}} + C

Solution steps

\int 2 8 x d x

Take the constant out:

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

= 2 \cdot \int 8 x d x

Simplify

8 x : 22 x

= 2 \cdot \int 22 x d x

Take the constant out:

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

= 2 \cdot 22 \cdot \int x d x

Apply the Power Rule

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

= 2 \cdot 22 \frac{2}{3} x^{\frac{3}{2}}

Simplify

2 \cdot 22 \frac{2}{3} x^{\frac{3}{2}} : \frac{8 2}{3} x^{\frac{3}{2}}

= \frac{8 2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{8 2}{3} x^{\frac{3}{2}} + C

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