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

The integral of 2sqrt(x^3) is 4/5 x^{5/2}+C

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integral of 2sqrt(x^3)

\int 2 x^{3} d x

\frac{4}{5} x^{\frac{5}{2}} + C

Solution steps

\int 2 x^{3} d x

Take the constant out:

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

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

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

assuming

x \geq 0

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

Apply the Power Rule

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

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

Simplify

2 \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{4}{5} x^{\frac{5}{2}}

= \frac{4}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{4}{5} x^{\frac{5}{2}} + C

(\frac{2}{t})^{^{'}}

\frac{1}{5 x + 7}

y^{^{'}} = 2 y - y^{3}

\int \frac{1}{x ^{2} - 3} d x

y^{^{'}} = x + 3 y

What is the integral of 2sqrt(x^3) ?
The integral of 2sqrt(x^3) is 4/5 x^{5/2}+C