Optimal. Leaf size=25 \[ -\frac {x^5}{5}+\frac {x^{10}}{10}+\frac {1}{5} \log \left (1+x^5\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {272, 45}
\begin {gather*} \frac {x^{10}}{10}-\frac {x^5}{5}+\frac {1}{5} \log \left (x^5+1\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 272
Rubi steps
\begin {align*} \int \frac {x^{14}}{1+x^5} \, dx &=\frac {1}{5} \text {Subst}\left (\int \frac {x^2}{1+x} \, dx,x,x^5\right )\\ &=\frac {1}{5} \text {Subst}\left (\int \left (-1+x+\frac {1}{1+x}\right ) \, dx,x,x^5\right )\\ &=-\frac {x^5}{5}+\frac {x^{10}}{10}+\frac {1}{5} \log \left (1+x^5\right )\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 22, normalized size = 0.88 \begin {gather*} \frac {1}{10} \left (-3-2 x^5+x^{10}+2 \log \left (1+x^5\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.19, size = 20, normalized size = 0.80
method | result | size |
default | \(-\frac {x^{5}}{5}+\frac {x^{10}}{10}+\frac {\ln \left (x^{5}+1\right )}{5}\) | \(20\) |
risch | \(-\frac {x^{5}}{5}+\frac {x^{10}}{10}+\frac {\ln \left (x^{5}+1\right )}{5}\) | \(20\) |
meijerg | \(-\frac {x^{5} \left (-3 x^{5}+6\right )}{30}+\frac {\ln \left (x^{5}+1\right )}{5}\) | \(22\) |
norman | \(-\frac {x^{5}}{5}+\frac {x^{10}}{10}+\frac {\ln \left (x +1\right )}{5}+\frac {\ln \left (x^{4}-x^{3}+x^{2}-x +1\right )}{5}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{10} \, x^{10} - \frac {1}{5} \, x^{5} + \frac {1}{5} \, \log \left (x^{5} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{10} \, x^{10} - \frac {1}{5} \, x^{5} + \frac {1}{5} \, \log \left (x^{5} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 17, normalized size = 0.68 \begin {gather*} \frac {x^{10}}{10} - \frac {x^{5}}{5} + \frac {\log {\left (x^{5} + 1 \right )}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.35, size = 20, normalized size = 0.80 \begin {gather*} \frac {1}{10} \, x^{10} - \frac {1}{5} \, x^{5} + \frac {1}{5} \, \log \left ({\left | x^{5} + 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 19, normalized size = 0.76 \begin {gather*} \frac {\ln \left (x^5+1\right )}{5}-\frac {x^5}{5}+\frac {x^{10}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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