Optimal. Leaf size=19 \[ 3 a \sqrt [3]{x}+\frac {3}{4} b x^{4/3} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45}
\begin {gather*} 3 a \sqrt [3]{x}+\frac {3}{4} b x^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {a+b x}{x^{2/3}} \, dx &=\int \left (\frac {a}{x^{2/3}}+b \sqrt [3]{x}\right ) \, dx\\ &=3 a \sqrt [3]{x}+\frac {3}{4} b x^{4/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 16, normalized size = 0.84 \begin {gather*} \frac {3}{4} \sqrt [3]{x} (4 a+b x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 14, normalized size = 0.74
method | result | size |
gosper | \(\frac {3 x^{\frac {1}{3}} \left (b x +4 a \right )}{4}\) | \(13\) |
trager | \(\left (\frac {3 b x}{4}+3 a \right ) x^{\frac {1}{3}}\) | \(13\) |
risch | \(\frac {3 x^{\frac {1}{3}} \left (b x +4 a \right )}{4}\) | \(13\) |
derivativedivides | \(3 a \,x^{\frac {1}{3}}+\frac {3 b \,x^{\frac {4}{3}}}{4}\) | \(14\) |
default | \(3 a \,x^{\frac {1}{3}}+\frac {3 b \,x^{\frac {4}{3}}}{4}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 0.68 \begin {gather*} \frac {3}{4} \, b x^{\frac {4}{3}} + 3 \, a x^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.52, size = 12, normalized size = 0.63 \begin {gather*} \frac {3}{4} \, {\left (b x + 4 \, a\right )} x^{\frac {1}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.46, size = 17, normalized size = 0.89 \begin {gather*} 3 a \sqrt [3]{x} + \frac {3 b x^{\frac {4}{3}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.32, size = 13, normalized size = 0.68 \begin {gather*} \frac {3}{4} \, b x^{\frac {4}{3}} + 3 \, a x^{\frac {1}{3}} \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 = 0.63 \begin {gather*} \frac {3\,x^{1/3}\,\left (4\,a+b\,x\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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