Optimal. Leaf size=15 \[ \frac {14 e^{e^x} x^2}{18+e} \]
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Rubi [A]
time = 0.02, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {12, 2326}
\begin {gather*} \frac {14 e^{e^x} x^2}{18+e} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int e^{e^x} \left (28 x+14 e^x x^2\right ) \, dx}{18+e}\\ &=\frac {14 e^{e^x} x^2}{18+e}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} \frac {14 e^{e^x} x^2}{18+e} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 15, normalized size = 1.00
method | result | size |
norman | \(\frac {14 x^{2} {\mathrm e}^{{\mathrm e}^{x}}}{{\mathrm e}+18}\) | \(15\) |
risch | \(\frac {14 x^{2} {\mathrm e}^{{\mathrm e}^{x}}}{{\mathrm e}+18}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 14, normalized size = 0.93 \begin {gather*} \frac {14 \, x^{2} e^{\left (e^{x}\right )}}{e + 18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 14, normalized size = 0.93 \begin {gather*} \frac {14 \, x^{2} e^{\left (e^{x}\right )}}{e + 18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 14, normalized size = 0.93 \begin {gather*} \frac {14 x^{2} e^{e^{x}}}{e + 18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 14, normalized size = 0.93 \begin {gather*} \frac {14 \, x^{2} e^{\left (e^{x}\right )}}{e + 18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.32, size = 14, normalized size = 0.93 \begin {gather*} \frac {14\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^x}}{\mathrm {e}+18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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