Optimal. Leaf size=27 \[ 2-\left (-5+2 x-x^2\right ) \left (x+3 \left (2+x+\frac {5}{\log (3)}\right )\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.11, 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 = {12}
\begin {gather*} 4 x^3-2 x^2+\frac {15 x^2}{\log (3)}+8 x-\frac {30 x}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-30+30 x+\left (8-4 x+12 x^2\right ) \log (3)\right ) \, dx}{\log (3)}\\ &=-\frac {30 x}{\log (3)}+\frac {15 x^2}{\log (3)}+\int \left (8-4 x+12 x^2\right ) \, dx\\ &=8 x-2 x^2+4 x^3-\frac {30 x}{\log (3)}+\frac {15 x^2}{\log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 33, normalized size = 1.22 \begin {gather*} \frac {-30 x+15 x^2+8 x \log (3)-2 x^2 \log (3)+4 x^3 \log (3)}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 34, normalized size = 1.26
method | result | size |
gosper | \(\frac {x \left (4 x^{2} \ln \left (3\right )-2 x \ln \left (3\right )+8 \ln \left (3\right )+15 x -30\right )}{\ln \left (3\right )}\) | \(28\) |
risch | \(4 x^{3}-2 x^{2}+8 x +\frac {15 x^{2}}{\ln \left (3\right )}-\frac {30 x}{\ln \left (3\right )}\) | \(31\) |
default | \(\frac {4 x^{3} \ln \left (3\right )-2 x^{2} \ln \left (3\right )+8 x \ln \left (3\right )+15 x^{2}-30 x}{\ln \left (3\right )}\) | \(34\) |
norman | \(4 x^{3}-\frac {\left (2 \ln \left (3\right )-15\right ) x^{2}}{\ln \left (3\right )}+\frac {2 \left (4 \ln \left (3\right )-15\right ) x}{\ln \left (3\right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 32, normalized size = 1.19 \begin {gather*} \frac {15 \, x^{2} + 2 \, {\left (2 \, x^{3} - x^{2} + 4 \, x\right )} \log \left (3\right ) - 30 \, x}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 32, normalized size = 1.19 \begin {gather*} \frac {15 \, x^{2} + 2 \, {\left (2 \, x^{3} - x^{2} + 4 \, x\right )} \log \left (3\right ) - 30 \, x}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 29, normalized size = 1.07 \begin {gather*} 4 x^{3} + \frac {x^{2} \cdot \left (15 - 2 \log {\left (3 \right )}\right )}{\log {\left (3 \right )}} + \frac {x \left (-30 + 8 \log {\left (3 \right )}\right )}{\log {\left (3 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 32, normalized size = 1.19 \begin {gather*} \frac {15 \, x^{2} + 2 \, {\left (2 \, x^{3} - x^{2} + 4 \, x\right )} \log \left (3\right ) - 30 \, x}{\log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.17, size = 31, normalized size = 1.15 \begin {gather*} 4\,x^3-\frac {\left (\ln \left (81\right )-30\right )\,x^2}{2\,\ln \left (3\right )}+\frac {\left (8\,\ln \left (3\right )-30\right )\,x}{\ln \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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