Optimal. Leaf size=16 \[ \frac {3 (a+b x)^{2/3}}{2 b} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {32} \begin {gather*} \frac {3 (a+b x)^{2/3}}{2 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int \frac {1}{\sqrt [3]{a+b x}} \, dx &=\frac {3 (a+b x)^{2/3}}{2 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} \frac {3 (a+b x)^{2/3}}{2 b} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} \frac {3 (a+b x)^{2/3}}{2 b} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 12, normalized size = 0.75 \begin {gather*} \frac {3 \, {\left (b x + a\right )}^{\frac {2}{3}}}{2 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.97, size = 12, normalized size = 0.75 \begin {gather*} \frac {3 \, {\left (b x + a\right )}^{\frac {2}{3}}}{2 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \begin {gather*} \frac {3 \left (b x +a \right )^{\frac {2}{3}}}{2 b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 12, normalized size = 0.75 \begin {gather*} \frac {3 \, {\left (b x + a\right )}^{\frac {2}{3}}}{2 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 12, normalized size = 0.75 \begin {gather*} \frac {3\,{\left (a+b\,x\right )}^{2/3}}{2\,b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 12, normalized size = 0.75 \begin {gather*} \frac {3 \left (a + b x\right )^{\frac {2}{3}}}{2 b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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