Optimal. Leaf size=16 \[ \frac {4 \left (x+x^6\right )^{3/4}}{3 x^3} \]
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Rubi [A]
time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {1604}
\begin {gather*} \frac {4 \left (x^6+x\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 1604
Rubi steps
\begin {align*} \int \frac {-3+2 x^5}{x^3 \sqrt [4]{x+x^6}} \, dx &=\frac {4 \left (x+x^6\right )^{3/4}}{3 x^3}\\ \end {align*}
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Mathematica [A]
time = 10.01, size = 16, normalized size = 1.00 \begin {gather*} \frac {4 \left (x+x^6\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.28, size = 13, normalized size = 0.81
method | result | size |
trager | \(\frac {4 \left (x^{6}+x \right )^{\frac {3}{4}}}{3 x^{3}}\) | \(13\) |
risch | \(\frac {\frac {4 x^{5}}{3}+\frac {4}{3}}{x^{2} \left (x \left (x^{5}+1\right )\right )^{\frac {1}{4}}}\) | \(20\) |
gosper | \(\frac {4 \left (x^{4}-x^{3}+x^{2}-x +1\right ) \left (1+x \right )}{3 x^{2} \left (x^{6}+x \right )^{\frac {1}{4}}}\) | \(32\) |
meijerg | \(\frac {4 \hypergeom \left (\left [-\frac {9}{20}, \frac {1}{4}\right ], \left [\frac {11}{20}\right ], -x^{5}\right )}{3 x^{\frac {9}{4}}}+\frac {8 x^{\frac {11}{4}} \hypergeom \left (\left [\frac {1}{4}, \frac {11}{20}\right ], \left [\frac {31}{20}\right ], -x^{5}\right )}{11}\) | \(34\) |
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 = 12, normalized size = 0.75 \begin {gather*} \frac {4 \, {\left (x^{6} + x\right )}^{\frac {3}{4}}}{3 \, x^{3}} \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 {2 x^{5} - 3}{x^{3} \sqrt [4]{x \left (x + 1\right ) \left (x^{4} - x^{3} + x^{2} - 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 = 0.25, size = 12, normalized size = 0.75 \begin {gather*} \frac {4\,{\left (x^6+x\right )}^{3/4}}{3\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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