What is the integral of sqrt(2x^3) ?

The integral of sqrt(2x^3) is sqrt(2) 2/5 x^{5/2}+C

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integral of sqrt(2x^3)

\int 2 x^{3} d x

2 \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

\int 2 x^{3} d x

Simplify

2 x^{3} : 2 x x^{2}

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

Take the constant out:

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

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

x^{2} = (x),

assuming

x \geq 0

= 2 \cdot \int x x d x

Simplify

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

= 2 \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

: \frac{2}{5} x^{\frac{5}{2}}

= 2 \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= 2 \frac{2}{5} x^{\frac{5}{2}} + C

x \to \infty lim (- e^{x})

\int e^{2 x} 1 - 4 e^{2 x} d x

\int 2 sin^{3} (3 x) cos^{3} (3 x) d x

x \to \infty lim (\frac{4 x - 5}{2 x + 3})

n = 1 \sum \infty \frac{4 n}{4 n + 7}

What is the integral of sqrt(2x^3) ?
The integral of sqrt(2x^3) is sqrt(2) 2/5 x^{5/2}+C