Optimal. Leaf size=34 \[ -3+x \left (x \left (-e^2+x\right )-\frac {-5+e^{e^{2 x}}+\log \left (-\frac {1}{4}+x\right )}{x}\right ) \]
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Rubi [A] time = 0.18, antiderivative size = 29, normalized size of antiderivative = 0.85, number of steps used = 6, number of rules used = 4, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {6742, 2282, 2194, 1850} \begin {gather*} x^3-e^2 x^2-e^{e^{2 x}}-\log (1-4 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1850
Rule 2194
Rule 2282
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 e^{e^{2 x}+2 x}+\frac {4-2 e^2 x+\left (3+8 e^2\right ) x^2-12 x^3}{1-4 x}\right ) \, dx\\ &=-\left (2 \int e^{e^{2 x}+2 x} \, dx\right )+\int \frac {4-2 e^2 x+\left (3+8 e^2\right ) x^2-12 x^3}{1-4 x} \, dx\\ &=\int \left (-2 e^2 x+3 x^2-\frac {4}{-1+4 x}\right ) \, dx-\operatorname {Subst}\left (\int e^x \, dx,x,e^{2 x}\right )\\ &=-e^{e^{2 x}}-e^2 x^2+x^3-\log (1-4 x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 29, normalized size = 0.85 \begin {gather*} -e^{e^{2 x}}-e^2 x^2+x^3-\log (1-4 x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 45, normalized size = 1.32 \begin {gather*} {\left ({\left (x^{3} - x^{2} e^{2}\right )} e^{\left (2 \, x\right )} - e^{\left (2 \, x\right )} \log \left (4 \, x - 1\right ) - e^{\left (2 \, x + e^{\left (2 \, x\right )}\right )}\right )} e^{\left (-2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 48, normalized size = 1.41 \begin {gather*} {\left (x^{3} e^{\left (2 \, x\right )} - x^{2} e^{\left (2 \, x + 2\right )} - e^{\left (2 \, x\right )} \log \left (4 \, x - 1\right ) - e^{\left (2 \, x + e^{\left (2 \, x\right )}\right )}\right )} e^{\left (-2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.32, size = 27, normalized size = 0.79
method | result | size |
norman | \(x^{3}-x^{2} {\mathrm e}^{2}-{\mathrm e}^{{\mathrm e}^{2 x}}-\ln \left (4 x -1\right )\) | \(27\) |
risch | \(x^{3}-x^{2} {\mathrm e}^{2}-{\mathrm e}^{{\mathrm e}^{2 x}}-\ln \left (4 x -1\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 52, normalized size = 1.53 \begin {gather*} x^{3} - \frac {1}{8} \, {\left (8 \, x^{2} + 4 \, x + \log \left (4 \, x - 1\right )\right )} e^{2} + \frac {1}{8} \, {\left (4 \, x + \log \left (4 \, x - 1\right )\right )} e^{2} - e^{\left (e^{\left (2 \, x\right )}\right )} - \log \left (4 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.41, size = 24, normalized size = 0.71 \begin {gather*} x^3-{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}-x^2\,{\mathrm {e}}^2-\ln \left (x-\frac {1}{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 22, normalized size = 0.65 \begin {gather*} x^{3} - x^{2} e^{2} - e^{e^{2 x}} - \log {\left (4 x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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