What is the integral of 4sqrt(x^3) ?

The integral of 4sqrt(x^3) is 8/5 x^{5/2}+C

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integral of 4sqrt(x^3)

\int 4 x^{3} d x

\frac{8}{5} x^{\frac{5}{2}} + C

Solution steps

\int 4 x^{3} d x

Take the constant out:

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

= 4 \cdot \int x^{3} d x

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

assuming

x \geq 0

= 4 \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

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

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

Simplify

4 \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{8}{5} x^{\frac{5}{2}}

= \frac{8}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{8}{5} x^{\frac{5}{2}} + C

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What is the integral of 4sqrt(x^3) ?
The integral of 4sqrt(x^3) is 8/5 x^{5/2}+C