Optimal. Leaf size=16 \[ -\frac {\left (1+x^3\right )^{4/3}}{4 x^4} \]
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Rubi [A]
time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {270}
\begin {gather*} -\frac {\left (x^3+1\right )^{4/3}}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\sqrt [3]{1+x^3}}{x^5} \, dx &=-\frac {\left (1+x^3\right )^{4/3}}{4 x^4}\\ \end {align*}
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Mathematica [A]
time = 0.05, size = 16, normalized size = 1.00 \begin {gather*} -\frac {\left (1+x^3\right )^{4/3}}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.25, size = 13, normalized size = 0.81
method | result | size |
trager | \(-\frac {\left (x^{3}+1\right )^{\frac {4}{3}}}{4 x^{4}}\) | \(13\) |
meijerg | \(-\frac {\left (x^{3}+1\right )^{\frac {4}{3}}}{4 x^{4}}\) | \(13\) |
risch | \(-\frac {x^{6}+2 x^{3}+1}{4 \left (x^{3}+1\right )^{\frac {2}{3}} x^{4}}\) | \(23\) |
gosper | \(-\frac {\left (1+x \right ) \left (x^{2}-x +1\right ) \left (x^{3}+1\right )^{\frac {1}{3}}}{4 x^{4}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 12, normalized size = 0.75 \begin {gather*} -\frac {{\left (x^{3} + 1\right )}^{\frac {4}{3}}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 12, normalized size = 0.75 \begin {gather*} -\frac {{\left (x^{3} + 1\right )}^{\frac {4}{3}}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 53 vs.
\(2 (14) = 28\).
time = 0.39, size = 53, normalized size = 3.31 \begin {gather*} \frac {\sqrt [3]{1 + \frac {1}{x^{3}}} \Gamma \left (- \frac {4}{3}\right )}{3 \Gamma \left (- \frac {1}{3}\right )} + \frac {\sqrt [3]{1 + \frac {1}{x^{3}}} \Gamma \left (- \frac {4}{3}\right )}{3 x^{3} \Gamma \left (- \frac {1}{3}\right )} \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 = 0.19, size = 24, normalized size = 1.50 \begin {gather*} -\frac {{\left (x^3+1\right )}^{1/3}+x^3\,{\left (x^3+1\right )}^{1/3}}{4\,x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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