Optimal. Leaf size=25 \[ x^2 \left (4-e^{e^x}-x-17 x (3-\log (x))\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 28, normalized size of antiderivative = 1.12, number of steps used = 3, number of rules used = 2, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2288, 2304} \begin {gather*} -52 x^3+17 x^3 \log (x)-e^{e^x} x^2+4 x^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 x^2-\frac {139 x^3}{3}+51 \int x^2 \log (x) \, dx+\int e^{e^x} \left (-2 x-e^x x^2\right ) \, dx\\ &=4 x^2-e^{e^x} x^2-52 x^3+17 x^3 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 21, normalized size = 0.84 \begin {gather*} x^2 \left (4-e^{e^x}-52 x+17 x \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 26, normalized size = 1.04 \begin {gather*} 17 \, x^{3} \log \relax (x) - 52 \, x^{3} - x^{2} e^{\left (e^{x}\right )} + 4 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 26, normalized size = 1.04 \begin {gather*} 17 \, x^{3} \log \relax (x) - 52 \, x^{3} - x^{2} e^{\left (e^{x}\right )} + 4 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 27, normalized size = 1.08
method | result | size |
default | \(-{\mathrm e}^{{\mathrm e}^{x}} x^{2}+4 x^{2}-52 x^{3}+17 x^{3} \ln \relax (x )\) | \(27\) |
risch | \(-{\mathrm e}^{{\mathrm e}^{x}} x^{2}+4 x^{2}-52 x^{3}+17 x^{3} \ln \relax (x )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 26, normalized size = 1.04 \begin {gather*} 17 \, x^{3} \log \relax (x) - 52 \, x^{3} - x^{2} e^{\left (e^{x}\right )} + 4 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.16, size = 18, normalized size = 0.72 \begin {gather*} -x^2\,\left (52\,x+{\mathrm {e}}^{{\mathrm {e}}^x}-17\,x\,\ln \relax (x)-4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 26, normalized size = 1.04 \begin {gather*} 17 x^{3} \log {\relax (x )} - 52 x^{3} - x^{2} e^{e^{x}} + 4 x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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