Optimal. Leaf size=14 \[ \frac {1}{2} x \sqrt [3]{b x^3} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30} \[ \frac {1}{2} x \sqrt [3]{b x^3} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \sqrt [3]{b x^3} \, dx &=\frac {\sqrt [3]{b x^3} \int x \, dx}{x}\\ &=\frac {1}{2} x \sqrt [3]{b x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ \frac {1}{2} x \sqrt [3]{b x^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 10, normalized size = 0.71 \[ \frac {1}{2} \, \left (b x^{3}\right )^{\frac {1}{3}} x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 8, normalized size = 0.57 \[ \frac {1}{2} \, b^{\frac {1}{3}} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.79 \[ \frac {\left (b \,x^{3}\right )^{\frac {1}{3}} x}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 10, normalized size = 0.71 \[ \frac {1}{2} \, \left (b x^{3}\right )^{\frac {1}{3}} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.07 \[ \int {\left (b\,x^3\right )}^{1/3} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 14, normalized size = 1.00 \[ \frac {\sqrt [3]{b} x \sqrt [3]{x^{3}}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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