Optimal. Leaf size=15 \[ 1029-x+x^4 (1+\log (4))^2 \]
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Rubi [A]
time = 0.01, antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps
used = 3, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {6}
\begin {gather*} x^4 (1+\log (4))^2-x \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+4 x^3 \log ^2(4)+x^3 (4+8 \log (4))\right ) \, dx\\ &=\int \left (-1+x^3 \left (4+8 \log (4)+4 \log ^2(4)\right )\right ) \, dx\\ &=-x+x^4 (1+\log (4))^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 22, normalized size = 1.47 \begin {gather*} -x+x^4+2 x^4 \log (4)+x^4 \log ^2(4) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.16, size = 24, normalized size = 1.60
method | result | size |
norman | \(\left (4 \ln \left (2\right )^{2}+4 \ln \left (2\right )+1\right ) x^{4}-x\) | \(21\) |
gosper | \(4 x^{4} \ln \left (2\right )^{2}+4 x^{4} \ln \left (2\right )+x^{4}-x\) | \(24\) |
default | \(4 x^{4} \ln \left (2\right )^{2}+4 x^{4} \ln \left (2\right )+x^{4}-x\) | \(24\) |
risch | \(4 x^{4} \ln \left (2\right )^{2}+4 x^{4} \ln \left (2\right )+x^{4}-x\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 23, normalized size = 1.53 \begin {gather*} 4 \, x^{4} \log \left (2\right )^{2} + 4 \, x^{4} \log \left (2\right ) + x^{4} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 23, normalized size = 1.53 \begin {gather*} 4 \, x^{4} \log \left (2\right )^{2} + 4 \, x^{4} \log \left (2\right ) + x^{4} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 17, normalized size = 1.13 \begin {gather*} x^{4} \cdot \left (1 + 4 \log {\left (2 \right )}^{2} + 4 \log {\left (2 \right )}\right ) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 23, normalized size = 1.53 \begin {gather*} 4 \, x^{4} \log \left (2\right )^{2} + 4 \, x^{4} \log \left (2\right ) + x^{4} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 18, normalized size = 1.20 \begin {gather*} x^4\,\left (\ln \left (16\right )+4\,{\ln \left (2\right )}^2+1\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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