3.20 \(\int x^{3/2} \, dx\)

Optimal. Leaf size=9 \[ \frac{2 x^{5/2}}{5} \]

[Out]

(2*x^(5/2))/5

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Rubi [A]  time = 0.0004782, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {30} \[ \frac{2 x^{5/2}}{5} \]

Antiderivative was successfully verified.

[In]

Int[x^(3/2),x]

[Out]

(2*x^(5/2))/5

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin{align*} \int x^{3/2} \, dx &=\frac{2 x^{5/2}}{5}\\ \end{align*}

Mathematica [A]  time = 0.0005174, size = 9, normalized size = 1. \[ \frac{2 x^{5/2}}{5} \]

Antiderivative was successfully verified.

[In]

Integrate[x^(3/2),x]

[Out]

(2*x^(5/2))/5

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Maple [A]  time = 0.001, size = 6, normalized size = 0.7 \begin{align*}{\frac{2}{5}{x}^{{\frac{5}{2}}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^(3/2),x)

[Out]

2/5*x^(5/2)

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Maxima [A]  time = 0.927467, size = 7, normalized size = 0.78 \begin{align*} \frac{2}{5} \, x^{\frac{5}{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(3/2),x, algorithm="maxima")

[Out]

2/5*x^(5/2)

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Fricas [A]  time = 1.7388, size = 18, normalized size = 2. \begin{align*} \frac{2}{5} \, x^{\frac{5}{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(3/2),x, algorithm="fricas")

[Out]

2/5*x^(5/2)

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Sympy [A]  time = 0.052248, size = 7, normalized size = 0.78 \begin{align*} \frac{2 x^{\frac{5}{2}}}{5} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**(3/2),x)

[Out]

2*x**(5/2)/5

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Giac [A]  time = 1.0807, size = 7, normalized size = 0.78 \begin{align*} \frac{2}{5} \, x^{\frac{5}{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(3/2),x, algorithm="giac")

[Out]

2/5*x^(5/2)