Optimal. Leaf size=13 \[ \frac {3}{4} \left (x^3+x\right )^{4/3} \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {1588} \begin {gather*} \frac {3}{4} \left (x^3+x\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin {align*} \int \left (1+3 x^2\right ) \sqrt [3]{x+x^3} \, dx &=\frac {3}{4} \left (x+x^3\right )^{4/3}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 19, normalized size = 1.46 \begin {gather*} \frac {3}{4} x \left (x^2+1\right ) \sqrt [3]{x^3+x} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 13, normalized size = 1.00 \begin {gather*} \frac {3}{4} \left (x^3+x\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{4} \, {\left (x^{3} + x\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{4} \, {\left (x^{3} + x\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 1.23 \begin {gather*} \frac {3 \left (x^{2}+1\right ) x \left (x^{3}+x \right )^{\frac {1}{3}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 9, normalized size = 0.69 \begin {gather*} \frac {3}{4} \, {\left (x^{3} + x\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 9, normalized size = 0.69 \begin {gather*} \frac {3\,{\left (x^3+x\right )}^{4/3}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.17, size = 27, normalized size = 2.08 \begin {gather*} \frac {3 x^{3} \sqrt [3]{x^{3} + x}}{4} + \frac {3 x \sqrt [3]{x^{3} + x}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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