Optimal. Leaf size=18 \[ \frac {2 \left (a+b x^3\right )^{3/2}}{9 b} \]
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Rubi [A]
time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {267}
\begin {gather*} \frac {2 \left (a+b x^3\right )^{3/2}}{9 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int x^2 \sqrt {a+b x^3} \, dx &=\frac {2 \left (a+b x^3\right )^{3/2}}{9 b}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 18, normalized size = 1.00 \begin {gather*} \frac {2 \left (a+b x^3\right )^{3/2}}{9 b} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 15, normalized size = 0.83
method | result | size |
gosper | \(\frac {2 \left (b \,x^{3}+a \right )^{\frac {3}{2}}}{9 b}\) | \(15\) |
derivativedivides | \(\frac {2 \left (b \,x^{3}+a \right )^{\frac {3}{2}}}{9 b}\) | \(15\) |
default | \(\frac {2 \left (b \,x^{3}+a \right )^{\frac {3}{2}}}{9 b}\) | \(15\) |
trager | \(\frac {2 \left (b \,x^{3}+a \right )^{\frac {3}{2}}}{9 b}\) | \(15\) |
risch | \(\frac {2 \left (b \,x^{3}+a \right )^{\frac {3}{2}}}{9 b}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 14, normalized size = 0.78 \begin {gather*} \frac {2 \, {\left (b x^{3} + a\right )}^{\frac {3}{2}}}{9 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 14, normalized size = 0.78 \begin {gather*} \frac {2 \, {\left (b x^{3} + a\right )}^{\frac {3}{2}}}{9 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 42 vs.
\(2 (14) = 28\).
time = 0.07, size = 42, normalized size = 2.33 \begin {gather*} \begin {cases} \frac {2 a \sqrt {a + b x^{3}}}{9 b} + \frac {2 x^{3} \sqrt {a + b x^{3}}}{9} & \text {for}\: b \neq 0 \\\frac {\sqrt {a} x^{3}}{3} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.43, size = 14, normalized size = 0.78 \begin {gather*} \frac {2 \, {\left (b x^{3} + a\right )}^{\frac {3}{2}}}{9 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.09, size = 14, normalized size = 0.78 \begin {gather*} \frac {2\,{\left (b\,x^3+a\right )}^{3/2}}{9\,b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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