Optimal. Leaf size=20 \[ \frac {x^4}{12}-\frac {1}{18} \log \left (2+3 x^4\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {272, 45}
\begin {gather*} \frac {x^4}{12}-\frac {1}{18} \log \left (3 x^4+2\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 272
Rubi steps
\begin {align*} \int \frac {x^7}{2+3 x^4} \, dx &=\frac {1}{4} \text {Subst}\left (\int \frac {x}{2+3 x} \, dx,x,x^4\right )\\ &=\frac {1}{4} \text {Subst}\left (\int \left (\frac {1}{3}-\frac {2}{3 (2+3 x)}\right ) \, dx,x,x^4\right )\\ &=\frac {x^4}{12}-\frac {1}{18} \log \left (2+3 x^4\right )\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 21, normalized size = 1.05 \begin {gather*} \frac {1}{36} \left (2+3 x^4-2 \log \left (2+3 x^4\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 17, normalized size = 0.85
method | result | size |
default | \(\frac {x^{4}}{12}-\frac {\ln \left (3 x^{4}+2\right )}{18}\) | \(17\) |
norman | \(\frac {x^{4}}{12}-\frac {\ln \left (3 x^{4}+2\right )}{18}\) | \(17\) |
meijerg | \(\frac {x^{4}}{12}-\frac {\ln \left (1+\frac {3 x^{4}}{2}\right )}{18}\) | \(17\) |
risch | \(\frac {x^{4}}{12}-\frac {\ln \left (3 x^{4}+2\right )}{18}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{12} \, x^{4} - \frac {1}{18} \, \log \left (3 \, x^{4} + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{12} \, x^{4} - \frac {1}{18} \, \log \left (3 \, x^{4} + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 14, normalized size = 0.70 \begin {gather*} \frac {x^{4}}{12} - \frac {\log {\left (3 x^{4} + 2 \right )}}{18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.61, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{12} \, x^{4} - \frac {1}{18} \, \log \left (3 \, x^{4} + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 14, normalized size = 0.70 \begin {gather*} \frac {x^4}{12}-\frac {\ln \left (x^4+\frac {2}{3}\right )}{18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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