Optimal. Leaf size=14 \[ \frac {4 x}{\sqrt [4]{(-1+x) x^2}} \]
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Rubi [A]
time = 0.04, antiderivative size = 16, normalized size of antiderivative = 1.14, number of steps
used = 2, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2081, 75}
\begin {gather*} \frac {4 x}{\sqrt [4]{x^3-x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 75
Rule 2081
Rubi steps
\begin {align*} \int \frac {-2+x}{(-1+x) \sqrt [4]{-x^2+x^3}} \, dx &=\frac {\left (\sqrt [4]{-1+x} \sqrt {x}\right ) \int \frac {-2+x}{(-1+x)^{5/4} \sqrt {x}} \, dx}{\sqrt [4]{-x^2+x^3}}\\ &=\frac {4 x}{\sqrt [4]{-x^2+x^3}}\\ \end {align*}
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Mathematica [A]
time = 1.92, size = 14, normalized size = 1.00 \begin {gather*} \frac {4 x}{\sqrt [4]{(-1+x) x^2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.42, size = 13, normalized size = 0.93
method | result | size |
risch | \(\frac {4 x}{\left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{4}}}\) | \(13\) |
gosper | \(\frac {4 x}{\left (x^{3}-x^{2}\right )^{\frac {1}{4}}}\) | \(15\) |
trager | \(\frac {4 \left (x^{3}-x^{2}\right )^{\frac {3}{4}}}{\left (-1+x \right ) x}\) | \(22\) |
meijerg | \(\frac {4 \left (-\mathrm {signum}\left (-1+x \right )\right )^{\frac {1}{4}} \sqrt {x}\, \hypergeom \left (\left [\frac {1}{2}, \frac {5}{4}\right ], \left [\frac {3}{2}\right ], x\right )}{\mathrm {signum}\left (-1+x \right )^{\frac {1}{4}}}-\frac {2 \left (-\mathrm {signum}\left (-1+x \right )\right )^{\frac {1}{4}} x^{\frac {3}{2}} \hypergeom \left (\left [\frac {5}{4}, \frac {3}{2}\right ], \left [\frac {5}{2}\right ], x\right )}{3 \mathrm {signum}\left (-1+x \right )^{\frac {1}{4}}}\) | \(54\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 22, normalized size = 1.57 \begin {gather*} \frac {4 \, {\left (x^{3} - x^{2}\right )}^{\frac {3}{4}}}{x^{2} - x} \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 - 2}{\sqrt [4]{x^{2} \left (x - 1\right )} \left (x - 1\right )}\, 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 = 0.16, size = 21, normalized size = 1.50 \begin {gather*} \frac {4\,{\left (x^3-x^2\right )}^{3/4}}{x\,\left (x-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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