Optimal. Leaf size=12 \[ \frac {3}{4} \log \left (1+x^{4/3}\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {1607, 266}
\begin {gather*} \frac {3}{4} \log \left (x^{4/3}+1\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 266
Rule 1607
Rubi steps
\begin {align*} \int \frac {1}{\frac {1}{\sqrt [3]{x}}+x} \, dx &=\int \frac {\sqrt [3]{x}}{1+x^{4/3}} \, dx\\ &=\frac {3}{4} \log \left (1+x^{4/3}\right )\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} \frac {3}{4} \log \left (1+x^{4/3}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 9, normalized size = 0.75
method | result | size |
derivativedivides | \(\frac {3 \ln \left (1+x^{\frac {4}{3}}\right )}{4}\) | \(9\) |
default | \(\frac {3 \ln \left (1+x^{\frac {4}{3}}\right )}{4}\) | \(9\) |
meijerg | \(\frac {3 \ln \left (1+x^{\frac {4}{3}}\right )}{4}\) | \(9\) |
trager | \(-\frac {\ln \left (\frac {3 x^{\frac {20}{3}}-x^{8}-6 x^{\frac {16}{3}}-6 x^{\frac {8}{3}}+7 x^{4}+3 x^{\frac {4}{3}}-1}{\left (x^{4}+1\right )^{3}}\right )}{4}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 3.36, size = 8, normalized size = 0.67 \begin {gather*} \frac {3}{4} \, \log \left (x^{\frac {4}{3}} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.94, size = 8, normalized size = 0.67 \begin {gather*} \frac {3}{4} \, \log \left (x^{\frac {4}{3}} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 10, normalized size = 0.83 \begin {gather*} \frac {3 \log {\left (x^{\frac {4}{3}} + 1 \right )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 32 vs.
\(2 (8) = 16\).
time = 1.38, size = 32, normalized size = 2.67 \begin {gather*} \frac {3}{4} \, \log \left (\sqrt {2} x^{\frac {1}{3}} + x^{\frac {2}{3}} + 1\right ) + \frac {3}{4} \, \log \left (-\sqrt {2} x^{\frac {1}{3}} + x^{\frac {2}{3}} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.22, size = 8, normalized size = 0.67 \begin {gather*} \frac {3\,\ln \left (x^{4/3}+1\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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