Optimal. Leaf size=25 \[ \frac {\left (a x^3+b x^6\right )^{5/3}}{5 b x^5} \]
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Rubi [A] time = 0.00, antiderivative size = 25, 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 = {2000} \begin {gather*} \frac {\left (a x^3+b x^6\right )^{5/3}}{5 b x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 2000
Rubi steps
\begin {align*} \int \left (a x^3+b x^6\right )^{2/3} \, dx &=\frac {\left (a x^3+b x^6\right )^{5/3}}{5 b x^5}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 25, normalized size = 1.00 \begin {gather*} \frac {\left (x^3 \left (a+b x^3\right )\right )^{5/3}}{5 b x^5} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.20, size = 25, normalized size = 1.00 \begin {gather*} \frac {\left (a x^3+b x^6\right )^{5/3}}{5 b x^5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.91, size = 28, normalized size = 1.12 \begin {gather*} \frac {{\left (b x^{6} + a x^{3}\right )}^{\frac {2}{3}} {\left (b x^{3} + a\right )}}{5 \, b x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int {\left (b x^{6} + a x^{3}\right )}^{\frac {2}{3}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 29, normalized size = 1.16 \begin {gather*} \frac {\left (b \,x^{3}+a \right ) \left (b \,x^{6}+a \,x^{3}\right )^{\frac {2}{3}}}{5 b \,x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 14, normalized size = 0.56 \begin {gather*} \frac {{\left (b x^{3} + a\right )}^{\frac {5}{3}}}{5 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.15, size = 29, normalized size = 1.16 \begin {gather*} \frac {\left (\frac {a}{5\,b}+\frac {x^3}{5}\right )\,{\left (b\,x^6+a\,x^3\right )}^{2/3}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a x^{3} + b x^{6}\right )^{\frac {2}{3}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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