Optimal. Leaf size=13 \[ \frac {3}{8} \left (1+x^2\right )^{4/3} \]
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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {267}
\begin {gather*} \frac {3}{8} \left (x^2+1\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int x \sqrt [3]{1+x^2} \, dx &=\frac {3}{8} \left (1+x^2\right )^{4/3}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {3}{8} \left (1+x^2\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 10, normalized size = 0.77
method | result | size |
gosper | \(\frac {3 \left (x^{2}+1\right )^{\frac {4}{3}}}{8}\) | \(10\) |
derivativedivides | \(\frac {3 \left (x^{2}+1\right )^{\frac {4}{3}}}{8}\) | \(10\) |
default | \(\frac {3 \left (x^{2}+1\right )^{\frac {4}{3}}}{8}\) | \(10\) |
risch | \(\frac {3 \left (x^{2}+1\right )^{\frac {4}{3}}}{8}\) | \(10\) |
trager | \(\left (\frac {3}{8}+\frac {3 x^{2}}{8}\right ) \left (x^{2}+1\right )^{\frac {1}{3}}\) | \(16\) |
meijerg | \(\frac {x^{2} \hypergeom \left (\left [-\frac {1}{3}, 1\right ], \left [2\right ], -x^{2}\right )}{2}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{8} \, {\left (x^{2} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{8} \, {\left (x^{2} + 1\right )}^{\frac {4}{3}} \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. 26 vs.
\(2 (10) = 20\).
time = 0.06, size = 26, normalized size = 2.00 \begin {gather*} \frac {3 x^{2} \sqrt [3]{x^{2} + 1}}{8} + \frac {3 \sqrt [3]{x^{2} + 1}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{8} \, {\left (x^{2} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 9, normalized size = 0.69 \begin {gather*} \frac {3\,{\left (x^2+1\right )}^{4/3}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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