Optimal. Leaf size=30 \[ 4 \sqrt {x}-\frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7}+2 \log (x) \]
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Rubi [A]
time = 0.07, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {1598, 1834}
\begin {gather*} -\frac {6 x^{7/6}}{7}-\frac {3 x^{2/3}}{2}+4 \sqrt {x}+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1598
Rule 1834
Rubi steps
\begin {align*} \int \frac {\left (2-x^{2/3}\right ) \left (\sqrt {x}+x\right )}{x^{3/2}} \, dx &=\int \frac {\left (1+\sqrt {x}\right ) \left (2-x^{2/3}\right )}{x} \, dx\\ &=-\left (6 \text {Subst}\left (\int \frac {\left (1+x^3\right ) \left (-2+x^4\right )}{x} \, dx,x,\sqrt [6]{x}\right )\right )\\ &=-\left (6 \text {Subst}\left (\int \left (-\frac {2}{x}-2 x^2+x^3+x^6\right ) \, dx,x,\sqrt [6]{x}\right )\right )\\ &=4 \sqrt {x}-\frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7}+2 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 30, normalized size = 1.00 \begin {gather*} 4 \sqrt {x}-\frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7}+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 21, normalized size = 0.70
method | result | size |
derivativedivides | \(-\frac {3 x^{\frac {2}{3}}}{2}-\frac {6 x^{\frac {7}{6}}}{7}+2 \ln \left (x \right )+4 \sqrt {x}\) | \(21\) |
default | \(-\frac {3 x^{\frac {2}{3}}}{2}-\frac {6 x^{\frac {7}{6}}}{7}+2 \ln \left (x \right )+4 \sqrt {x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 2.03, size = 20, normalized size = 0.67 \begin {gather*} -\frac {6}{7} \, x^{\frac {7}{6}} - \frac {3}{2} \, x^{\frac {2}{3}} + 4 \, \sqrt {x} + 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.46, size = 22, normalized size = 0.73 \begin {gather*} -\frac {6}{7} \, x^{\frac {7}{6}} - \frac {3}{2} \, x^{\frac {2}{3}} + 4 \, \sqrt {x} + 12 \, \log \left (x^{\frac {1}{6}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 2.06, size = 27, normalized size = 0.90 \begin {gather*} - \frac {6 x^{\frac {7}{6}}}{7} - \frac {3 x^{\frac {2}{3}}}{2} + 4 \sqrt {x} + 2 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.88, size = 21, normalized size = 0.70 \begin {gather*} -\frac {6}{7} \, x^{\frac {7}{6}} - \frac {3}{2} \, x^{\frac {2}{3}} + 4 \, \sqrt {x} + 2 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 22, normalized size = 0.73 \begin {gather*} 12\,\ln \left (x^{1/6}\right )+4\,\sqrt {x}-\frac {3\,x^{2/3}}{2}-\frac {6\,x^{7/6}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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