Optimal. Leaf size=18 \[ \frac {3 \left (a+b x^2\right )^{5/3}}{10 b} \]
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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 = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {267}
\begin {gather*} \frac {3 \left (a+b x^2\right )^{5/3}}{10 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int x \left (a+b x^2\right )^{2/3} \, dx &=\frac {3 \left (a+b x^2\right )^{5/3}}{10 b}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 18, normalized size = 1.00 \begin {gather*} \frac {3 \left (a+b x^2\right )^{5/3}}{10 b} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 15, normalized size = 0.83
method | result | size |
gosper | \(\frac {3 \left (b \,x^{2}+a \right )^{\frac {5}{3}}}{10 b}\) | \(15\) |
derivativedivides | \(\frac {3 \left (b \,x^{2}+a \right )^{\frac {5}{3}}}{10 b}\) | \(15\) |
default | \(\frac {3 \left (b \,x^{2}+a \right )^{\frac {5}{3}}}{10 b}\) | \(15\) |
trager | \(\frac {3 \left (b \,x^{2}+a \right )^{\frac {5}{3}}}{10 b}\) | \(15\) |
risch | \(\frac {3 \left (b \,x^{2}+a \right )^{\frac {5}{3}}}{10 b}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 14, normalized size = 0.78 \begin {gather*} \frac {3 \, {\left (b x^{2} + a\right )}^{\frac {5}{3}}}{10 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.07, size = 14, normalized size = 0.78 \begin {gather*} \frac {3 \, {\left (b x^{2} + a\right )}^{\frac {5}{3}}}{10 \, 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 = 0.09, size = 42, normalized size = 2.33 \begin {gather*} \begin {cases} \frac {3 a \left (a + b x^{2}\right )^{\frac {2}{3}}}{10 b} + \frac {3 x^{2} \left (a + b x^{2}\right )^{\frac {2}{3}}}{10} & \text {for}\: b \neq 0 \\\frac {a^{\frac {2}{3}} x^{2}}{2} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.92, size = 14, normalized size = 0.78 \begin {gather*} \frac {3 \, {\left (b x^{2} + a\right )}^{\frac {5}{3}}}{10 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.58, size = 14, normalized size = 0.78 \begin {gather*} \frac {3\,{\left (b\,x^2+a\right )}^{5/3}}{10\,b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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