Optimal. Leaf size=22 \[ -3-e^{4 x^2}+x-\frac {e^{e^x} x}{20} \]
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Rubi [A] time = 0.03, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps used = 4, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 2209, 2288} \begin {gather*} -e^{4 x^2}-\frac {1}{20} e^{e^x} x+x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2209
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{20} \int \left (20-160 e^{4 x^2} x+e^{e^x} \left (-1-e^x x\right )\right ) \, dx\\ &=x+\frac {1}{20} \int e^{e^x} \left (-1-e^x x\right ) \, dx-8 \int e^{4 x^2} x \, dx\\ &=-e^{4 x^2}+x-\frac {e^{e^x} x}{20}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.95 \begin {gather*} -e^{4 x^2}+x-\frac {e^{e^x} x}{20} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 16, normalized size = 0.73 \begin {gather*} -\frac {1}{20} \, x e^{\left (e^{x}\right )} + x - e^{\left (4 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 16, normalized size = 0.73 \begin {gather*} -\frac {1}{20} \, x e^{\left (e^{x}\right )} + x - e^{\left (4 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 17, normalized size = 0.77
method | result | size |
default | \(x -{\mathrm e}^{4 x^{2}}-\frac {x \,{\mathrm e}^{{\mathrm e}^{x}}}{20}\) | \(17\) |
norman | \(x -{\mathrm e}^{4 x^{2}}-\frac {x \,{\mathrm e}^{{\mathrm e}^{x}}}{20}\) | \(17\) |
risch | \(x -{\mathrm e}^{4 x^{2}}-\frac {x \,{\mathrm e}^{{\mathrm e}^{x}}}{20}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 16, normalized size = 0.73 \begin {gather*} -\frac {1}{20} \, x e^{\left (e^{x}\right )} + x - e^{\left (4 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.12, size = 16, normalized size = 0.73 \begin {gather*} x-{\mathrm {e}}^{4\,x^2}-\frac {x\,{\mathrm {e}}^{{\mathrm {e}}^x}}{20} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 15, normalized size = 0.68 \begin {gather*} - \frac {x e^{e^{x}}}{20} + x - e^{4 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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