Optimal. Leaf size=12 \[ \frac {3 \sqrt [3]{x}}{1+x} \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {75}
\begin {gather*} \frac {3 \sqrt [3]{x}}{x+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 75
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\frac {3 \sqrt [3]{x}}{1+x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 12, normalized size = 1.00 \begin {gather*} \frac {3 \sqrt [3]{x}}{1+x} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(31\) vs.
\(2(10)=20\).
time = 0.09, size = 32, normalized size = 2.67
method | result | size |
gosper | \(\frac {3 x^{\frac {1}{3}}}{x +1}\) | \(11\) |
trager | \(\frac {3 x^{\frac {1}{3}}}{x +1}\) | \(11\) |
risch | \(\frac {3 x^{\frac {1}{3}}}{x +1}\) | \(11\) |
derivativedivides | \(-\frac {-x^{\frac {1}{3}}-1}{x^{\frac {2}{3}}-x^{\frac {1}{3}}+1}-\frac {1}{1+x^{\frac {1}{3}}}\) | \(32\) |
default | \(-\frac {-x^{\frac {1}{3}}-1}{x^{\frac {2}{3}}-x^{\frac {1}{3}}+1}-\frac {1}{1+x^{\frac {1}{3}}}\) | \(32\) |
meijerg | \(\frac {3 x^{\frac {1}{3}}}{3+3 x}+\frac {2 \ln \left (1+x^{\frac {1}{3}}\right )}{3}-\frac {\ln \left (x^{\frac {2}{3}}-x^{\frac {1}{3}}+1\right )}{3}+\frac {2 \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, x^{\frac {1}{3}}}{2-x^{\frac {1}{3}}}\right )}{3}+\frac {2 x^{\frac {1}{3}}}{x +1}-\frac {2 x^{\frac {1}{3}} \left (\frac {\ln \left (1+x^{\frac {1}{3}}\right )}{x^{\frac {1}{3}}}-\frac {\ln \left (x^{\frac {2}{3}}-x^{\frac {1}{3}}+1\right )}{2 x^{\frac {1}{3}}}+\frac {\sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, x^{\frac {1}{3}}}{2-x^{\frac {1}{3}}}\right )}{x^{\frac {1}{3}}}\right )}{3}\) | \(125\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 10, normalized size = 0.83 \begin {gather*} \frac {3 \, x^{\frac {1}{3}}}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.56, size = 10, normalized size = 0.83 \begin {gather*} \frac {3 \, x^{\frac {1}{3}}}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.28, size = 8, normalized size = 0.67 \begin {gather*} \frac {3 \sqrt [3]{x}}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 10, normalized size = 0.83 \begin {gather*} \frac {3 \, x^{\frac {1}{3}}}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 10, normalized size = 0.83 \begin {gather*} \frac {3\,x^{1/3}}{x+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {not solved} \end {gather*}
Warning: Unable to verify antiderivative.
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