Optimal. Leaf size=29 \[ 4+e^2-x-x \left (-5+3 x^2 \left (\frac {3}{5}-\frac {4}{x}+\log (x)\right )\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 23, normalized size of antiderivative = 0.79, number of steps
used = 3, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {12, 2341}
\begin {gather*} -\frac {9 x^3}{5}-3 x^3 \log (x)+12 x^2+4 x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (20+120 x-42 x^2-45 x^2 \log (x)\right ) \, dx\\ &=4 x+12 x^2-\frac {14 x^3}{5}-9 \int x^2 \log (x) \, dx\\ &=4 x+12 x^2-\frac {9 x^3}{5}-3 x^3 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 23, normalized size = 0.79 \begin {gather*} 4 x+12 x^2-\frac {9 x^3}{5}-3 x^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 22, normalized size = 0.76
method | result | size |
default | \(12 x^{2}+4 x -\frac {9 x^{3}}{5}-3 x^{3} \ln \left (x \right )\) | \(22\) |
norman | \(12 x^{2}+4 x -\frac {9 x^{3}}{5}-3 x^{3} \ln \left (x \right )\) | \(22\) |
risch | \(12 x^{2}+4 x -\frac {9 x^{3}}{5}-3 x^{3} \ln \left (x \right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 21, normalized size = 0.72 \begin {gather*} -3 \, x^{3} \log \left (x\right ) - \frac {9}{5} \, x^{3} + 12 \, x^{2} + 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 21, normalized size = 0.72 \begin {gather*} -3 \, x^{3} \log \left (x\right ) - \frac {9}{5} \, x^{3} + 12 \, x^{2} + 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 22, normalized size = 0.76 \begin {gather*} - 3 x^{3} \log {\left (x \right )} - \frac {9 x^{3}}{5} + 12 x^{2} + 4 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 21, normalized size = 0.72 \begin {gather*} -3 \, x^{3} \log \left (x\right ) - \frac {9}{5} \, x^{3} + 12 \, x^{2} + 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.48, size = 21, normalized size = 0.72 \begin {gather*} 4\,x-3\,x^3\,\ln \left (x\right )+12\,x^2-\frac {9\,x^3}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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