Optimal. Leaf size=26 \[ 2-\frac {1}{25} e^{2 x^3+\frac {e^x x}{\log (5)}}-x \]
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Rubi [A]
time = 0.14, antiderivative size = 25, normalized size of antiderivative = 0.96, number of steps
used = 3, number of rules used = 2, integrand size = 51, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.039, Rules used = {12, 6838}
\begin {gather*} -\frac {1}{25} e^{2 x^3+\frac {e^x x}{\log (5)}}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-25 \log (5)+e^{\frac {e^x x+2 x^3 \log (5)}{\log (5)}} \left (e^x (-1-x)-6 x^2 \log (5)\right )\right ) \, dx}{25 \log (5)}\\ &=-x+\frac {\int e^{\frac {e^x x+2 x^3 \log (5)}{\log (5)}} \left (e^x (-1-x)-6 x^2 \log (5)\right ) \, dx}{25 \log (5)}\\ &=-\frac {1}{25} e^{2 x^3+\frac {e^x x}{\log (5)}}-x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.17, size = 25, normalized size = 0.96 \begin {gather*} -\frac {1}{25} e^{2 x^3+\frac {e^x x}{\log (5)}}-x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.22, size = 35, normalized size = 1.35
method | result | size |
risch | \(-x -\frac {{\mathrm e}^{\frac {x \left (2 x^{2} \ln \left (5\right )+{\mathrm e}^{x}\right )}{\ln \left (5\right )}}}{25}\) | \(24\) |
norman | \(-x -\frac {{\mathrm e}^{\frac {{\mathrm e}^{x} x +2 x^{3} \ln \left (5\right )}{\ln \left (5\right )}}}{25}\) | \(25\) |
default | \(\frac {-\ln \left (5\right ) {\mathrm e}^{\frac {{\mathrm e}^{x} x +2 x^{3} \ln \left (5\right )}{\ln \left (5\right )}}-25 x \ln \left (5\right )}{25 \ln \left (5\right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.56, size = 30, normalized size = 1.15 \begin {gather*} -\frac {25 \, x \log \left (5\right ) + e^{\left (2 \, x^{3} + \frac {x e^{x}}{\log \left (5\right )}\right )} \log \left (5\right )}{25 \, \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 24, normalized size = 0.92 \begin {gather*} -x - \frac {1}{25} \, e^{\left (\frac {2 \, x^{3} \log \left (5\right ) + x e^{x}}{\log \left (5\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 22, normalized size = 0.85 \begin {gather*} - x - \frac {e^{\frac {2 x^{3} \log {\left (5 \right )} + x e^{x}}{\log {\left (5 \right )}}}}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 30, normalized size = 1.15 \begin {gather*} -\frac {25 \, x \log \left (5\right ) + e^{\left (2 \, x^{3} + \frac {x e^{x}}{\log \left (5\right )}\right )} \log \left (5\right )}{25 \, \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.17, size = 21, normalized size = 0.81 \begin {gather*} -x-\frac {{\mathrm {e}}^{2\,x^3}\,{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^x}{\ln \left (5\right )}}}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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