What is the integral of sqrt(8x) ?

The integral of sqrt(8x) is (4sqrt(2))/3 x^{3/2}+C

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integral of sqrt(8x)

\int 8 x d x

\frac{4 2}{3} x^{\frac{3}{2}} + C

Solution steps

\int 8 x d x

Simplify

8 x : 22 x

= \int 22 x d x

Take the constant out:

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

= 22 \cdot \int x d x

Apply the Power Rule

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

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

Simplify

22 \frac{2}{3} x^{\frac{3}{2}} : \frac{4 2}{3} x^{\frac{3}{2}}

= \frac{4 2}{3} x^{\frac{3}{2}}

Add a constant to the solution

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

\frac{\partial}{\partial x} (x ln (x + 3 y))

\int \frac{- 4}{3 x ^{2}} d x

x \to 3 lim (\frac{x - 1}{3 - x})

x^{y} + 1

f (x) = e^{2 x} - x^{2} - 1

What is the integral of sqrt(8x) ?
The integral of sqrt(8x) is (4sqrt(2))/3 x^{3/2}+C