Optimal. Leaf size=29 \[ a^2 x+\frac {3}{2} a b x^{4/3}+\frac {3}{5} b^2 x^{5/3} \]
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Rubi [A] time = 0.02, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {190, 43} \[ a^2 x+\frac {3}{2} a b x^{4/3}+\frac {3}{5} b^2 x^{5/3} \]
Antiderivative was successfully verified.
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Rule 43
Rule 190
Rubi steps
\begin {align*} \int \left (a+b \sqrt [3]{x}\right )^2 \, dx &=3 \operatorname {Subst}\left (\int x^2 (a+b x)^2 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (a^2 x^2+2 a b x^3+b^2 x^4\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=a^2 x+\frac {3}{2} a b x^{4/3}+\frac {3}{5} b^2 x^{5/3}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 29, normalized size = 1.00 \[ a^2 x+\frac {3}{2} a b x^{4/3}+\frac {3}{5} b^2 x^{5/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 21, normalized size = 0.72 \[ \frac {3}{5} \, b^{2} x^{\frac {5}{3}} + \frac {3}{2} \, a b x^{\frac {4}{3}} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 21, normalized size = 0.72 \[ \frac {3}{5} \, b^{2} x^{\frac {5}{3}} + \frac {3}{2} \, a b x^{\frac {4}{3}} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 22, normalized size = 0.76 \[ \frac {3 b^{2} x^{\frac {5}{3}}}{5}+\frac {3 a b \,x^{\frac {4}{3}}}{2}+a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 21, normalized size = 0.72 \[ \frac {3}{5} \, b^{2} x^{\frac {5}{3}} + \frac {3}{2} \, a b x^{\frac {4}{3}} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 21, normalized size = 0.72 \[ a^2\,x+\frac {3\,b^2\,x^{5/3}}{5}+\frac {3\,a\,b\,x^{4/3}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.39, size = 27, normalized size = 0.93 \[ a^{2} x + \frac {3 a b x^{\frac {4}{3}}}{2} + \frac {3 b^{2} x^{\frac {5}{3}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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