Optimal. Leaf size=24 \[ 3 \left (16+e^{e^x}\right ) x^2 (x+\log (x) (-x+\log (\log (2)))) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(63\) vs. \(2(24)=48\).
time = 0.55, antiderivative size = 63, normalized size of antiderivative = 2.62, number of steps
used = 7, number of rules used = 4, integrand size = 86, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.047, Rules used = {2341, 6873, 12,
2326} \begin {gather*} 48 x^3-48 x^3 \log (x)+48 x^2 \log (\log (2)) \log (x)+3 e^{e^x-x} x \left (e^x x^2-e^x x^2 \log (x)+e^x x \log (\log (2)) \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rule 2341
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=32 x^3-144 \int x^2 \log (x) \, dx+\log (\log (2)) \int (48 x+96 x \log (x)) \, dx+\int e^{e^x} \left (6 x^2+3 e^x x^3+\left (-9 x^2-3 e^x x^3\right ) \log (x)+\left (3 x+\left (6 x+3 e^x x^2\right ) \log (x)\right ) \log (\log (2))\right ) \, dx\\ &=48 x^3-48 x^3 \log (x)+24 x^2 \log (\log (2))+(96 \log (\log (2))) \int x \log (x) \, dx+\int 3 e^{e^x} x \left (2 x+e^x x^2-3 x \log (x)-e^x x^2 \log (x)+\log (\log (2))+2 \log (x) \log (\log (2))+e^x x \log (x) \log (\log (2))\right ) \, dx\\ &=48 x^3-48 x^3 \log (x)+48 x^2 \log (x) \log (\log (2))+3 \int e^{e^x} x \left (2 x+e^x x^2-3 x \log (x)-e^x x^2 \log (x)+\log (\log (2))+2 \log (x) \log (\log (2))+e^x x \log (x) \log (\log (2))\right ) \, dx\\ &=48 x^3-48 x^3 \log (x)+48 x^2 \log (x) \log (\log (2))+3 e^{e^x-x} x \left (e^x x^2-e^x x^2 \log (x)+e^x x \log (x) \log (\log (2))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.21, size = 26, normalized size = 1.08 \begin {gather*} -3 \left (16+e^{e^x}\right ) x^2 (-x+\log (x) (x-\log (\log (2)))) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(50\) vs.
\(2(22)=44\).
time = 0.58, size = 51, normalized size = 2.12
method | result | size |
risch | \(\left (3 \ln \left (\ln \left (2\right )\right ) x^{2} \ln \left (x \right )-3 x^{3} \ln \left (x \right )+3 x^{3}\right ) {\mathrm e}^{{\mathrm e}^{x}}+48 \ln \left (\ln \left (2\right )\right ) x^{2} \ln \left (x \right )-48 x^{3} \ln \left (x \right )+48 x^{3}\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.61, size = 48, normalized size = 2.00 \begin {gather*} -48 \, x^{3} \log \left (x\right ) + 48 \, x^{2} \log \left (x\right ) \log \left (\log \left (2\right )\right ) + 48 \, x^{3} + 3 \, {\left (x^{3} - {\left (x^{3} - x^{2} \log \left (\log \left (2\right )\right )\right )} \log \left (x\right )\right )} e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 50 vs.
\(2 (24) = 48\).
time = 0.37, size = 50, normalized size = 2.08 \begin {gather*} -48 \, x^{3} \log \left (x\right ) + 48 \, x^{2} \log \left (x\right ) \log \left (\log \left (2\right )\right ) + 48 \, x^{3} - 3 \, {\left (x^{3} \log \left (x\right ) - x^{2} \log \left (x\right ) \log \left (\log \left (2\right )\right ) - x^{3}\right )} e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 54 vs.
\(2 (22) = 44\).
time = 5.59, size = 54, normalized size = 2.25 \begin {gather*} 48 x^{3} + \left (- 48 x^{3} + 48 x^{2} \log {\left (\log {\left (2 \right )} \right )}\right ) \log {\left (x \right )} + \left (- 3 x^{3} \log {\left (x \right )} + 3 x^{3} + 3 x^{2} \log {\left (x \right )} \log {\left (\log {\left (2 \right )} \right )}\right ) e^{e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 66 vs.
\(2 (24) = 48\).
time = 0.40, size = 66, normalized size = 2.75 \begin {gather*} -48 \, x^{3} \log \left (x\right ) + 48 \, x^{2} \log \left (x\right ) \log \left (\log \left (2\right )\right ) + 48 \, x^{3} - 3 \, {\left (x^{3} e^{\left (x + e^{x}\right )} \log \left (x\right ) - x^{2} e^{\left (x + e^{x}\right )} \log \left (x\right ) \log \left (\log \left (2\right )\right ) - x^{3} e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \ln \left (\ln \left (2\right )\right )\,\left (48\,x+96\,x\,\ln \left (x\right )\right )-144\,x^2\,\ln \left (x\right )+{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (3\,x^3\,{\mathrm {e}}^x+6\,x^2-\ln \left (x\right )\,\left (3\,x^3\,{\mathrm {e}}^x+9\,x^2\right )+\ln \left (\ln \left (2\right )\right )\,\left (3\,x+\ln \left (x\right )\,\left (6\,x+3\,x^2\,{\mathrm {e}}^x\right )\right )\right )+96\,x^2 \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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