Optimal. Leaf size=34 \[ e^x-e^{x \left (x+\frac {(-x+\log (3))^2}{x^2}\right )}-x+(1-2 x) x \]
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Rubi [A]
time = 0.20, antiderivative size = 28, normalized size of antiderivative = 0.82, number of steps
used = 4, number of rules used = 3, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.055, Rules used = {14, 2225, 6838}
\begin {gather*} -2 x^2-\frac {1}{9} e^{x^2+x+\frac {\log ^2(3)}{x}}+e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2225
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^x-4 x-\frac {e^{x+x^2+\frac {\log ^2(3)}{x}} \left (x^2+2 x^3-\log ^2(3)\right )}{9 x^2}\right ) \, dx\\ &=-2 x^2-\frac {1}{9} \int \frac {e^{x+x^2+\frac {\log ^2(3)}{x}} \left (x^2+2 x^3-\log ^2(3)\right )}{x^2} \, dx+\int e^x \, dx\\ &=e^x-\frac {1}{9} e^{x+x^2+\frac {\log ^2(3)}{x}}-2 x^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 28, normalized size = 0.82 \begin {gather*} e^x-\frac {1}{9} e^{x+x^2+\frac {\log ^2(3)}{x}}-2 x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 27, normalized size = 0.79
method | result | size |
risch | \(-2 x^{2}+{\mathrm e}^{x}-\frac {{\mathrm e}^{\frac {x^{3}+\ln \left (3\right )^{2}+x^{2}}{x}}}{9}\) | \(27\) |
norman | \(\frac {{\mathrm e}^{x} x -2 x^{3}-x \,{\mathrm e}^{\frac {\ln \left (3\right )^{2}-2 x \ln \left (3\right )+x^{3}+x^{2}}{x}}}{x}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 24, normalized size = 0.71 \begin {gather*} -2 \, x^{2} - \frac {1}{9} \, e^{\left (x^{2} + x + \frac {\log \left (3\right )^{2}}{x}\right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 31, normalized size = 0.91 \begin {gather*} -2 \, x^{2} + e^{x} - e^{\left (\frac {x^{3} + x^{2} - 2 \, x \log \left (3\right ) + \log \left (3\right )^{2}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 29, normalized size = 0.85 \begin {gather*} - 2 x^{2} + e^{x} - e^{\frac {x^{3} + x^{2} - 2 x \log {\left (3 \right )} + \log {\left (3 \right )}^{2}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 26, normalized size = 0.76 \begin {gather*} -2 \, x^{2} + e^{x} - \frac {1}{9} \, e^{\left (\frac {x^{3} + x^{2} + \log \left (3\right )^{2}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.38, size = 25, normalized size = 0.74 \begin {gather*} {\mathrm {e}}^x-2\,x^2-\frac {{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{\frac {{\ln \left (3\right )}^2}{x}}\,{\mathrm {e}}^x}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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