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

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

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integral of (sqrt(x^3))

\int (x^{3}) d x

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

Solution steps

\int x^{3} d x

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

assuming

x \geq 0

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

Apply the Power Rule

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

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

Add a constant to the solution

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

y = ln (x + 1)

\frac{d}{d x} ((sin (ln (x)))^{2})

\int \frac{6}{35 sin ( x ) - 12 cos ( x )} d x

y^{^{''}} + 2 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 0

t cos (3 t)

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