Optimal. Leaf size=18 \[ -\frac {3 \left (-1+x^2\right )^{2/3}}{2 (-1+x)^2} \]
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Rubi [A]
time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.11, number of steps
used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {801}
\begin {gather*} -\frac {3 \left (x^2-1\right )^{2/3}}{2 (1-x)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 801
Rubi steps
\begin {align*} \int \frac {3+x}{(-1+x)^2 \sqrt [3]{-1+x^2}} \, dx &=-\frac {3 \left (-1+x^2\right )^{2/3}}{2 (1-x)^2}\\ \end {align*}
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Mathematica [A]
time = 0.05, size = 18, normalized size = 1.00 \begin {gather*} -\frac {3 \left (-1+x^2\right )^{2/3}}{2 (-1+x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.48, size = 15, normalized size = 0.83
method | result | size |
trager | \(-\frac {3 \left (x^{2}-1\right )^{\frac {2}{3}}}{2 \left (-1+x \right )^{2}}\) | \(15\) |
gosper | \(-\frac {3 \left (1+x \right )}{2 \left (-1+x \right ) \left (x^{2}-1\right )^{\frac {1}{3}}}\) | \(18\) |
risch | \(-\frac {3 \left (1+x \right )}{2 \left (-1+x \right ) \left (x^{2}-1\right )^{\frac {1}{3}}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 12, normalized size = 0.67 \begin {gather*} -\frac {3 \, {\left (x + 1\right )}^{\frac {2}{3}}}{2 \, {\left (x - 1\right )}^{\frac {4}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 19, normalized size = 1.06 \begin {gather*} -\frac {3 \, {\left (x^{2} - 1\right )}^{\frac {2}{3}}}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x + 3}{\sqrt [3]{\left (x - 1\right ) \left (x + 1\right )} \left (x - 1\right )^{2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.14, size = 14, normalized size = 0.78 \begin {gather*} -\frac {3\,{\left (x^2-1\right )}^{2/3}}{2\,{\left (x-1\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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