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

The integral of 2x^3sqrt(x) is 4/9 x^{9/2}+C

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integral of 2x^3sqrt(x)

\int 2 x^{3} x d x

\frac{4}{9} x^{\frac{9}{2}} + C

Solution steps

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

Simplify

x^{3} x : x^{\frac{7}{2}}

= 2 \cdot \int x^{\frac{7}{2}} d x

Apply the Power Rule

: \frac{2}{9} x^{\frac{9}{2}}

= 2 \cdot \frac{2}{9} x^{\frac{9}{2}}

Simplify

2 \cdot \frac{2}{9} x^{\frac{9}{2}} : \frac{4}{9} x^{\frac{9}{2}}

= \frac{4}{9} x^{\frac{9}{2}}

Add a constant to the solution

= \frac{4}{9} x^{\frac{9}{2}} + C

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\frac{d x}{d t} = 2 x (7 - x)

\int_{0}^{1} \frac{( x - 1 )}{( x + 1 )} d x

What is the integral of 2x^3sqrt(x) ?
The integral of 2x^3sqrt(x) is 4/9 x^{9/2}+C