Optimal. Leaf size=23 \[ e^{x \left (3 (5-x)-\frac {e^{-x}}{\log (x)}\right )} \]
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Rubi [F]
time = 3.82, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\exp \left (-x+\frac {e^{-x} \left (-x+e^x \left (15 x-3 x^2\right ) \log (x)\right )}{\log (x)}\right ) \left (1+(-1+x) \log (x)+e^x (15-6 x) \log ^2(x)\right )}{\log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (-\frac {e^{-x} x \left (1-14 e^x \log (x)+3 e^x x \log (x)\right )}{\log (x)}\right ) \left (1+(-1+x) \log (x)+e^x (15-6 x) \log ^2(x)\right )}{\log ^2(x)} \, dx\\ &=\int \left (-3 \exp \left (x-\frac {e^{-x} x \left (1-14 e^x \log (x)+3 e^x x \log (x)\right )}{\log (x)}\right ) (-5+2 x)+\frac {\exp \left (-\frac {e^{-x} x \left (1-14 e^x \log (x)+3 e^x x \log (x)\right )}{\log (x)}\right ) (1-\log (x)+x \log (x))}{\log ^2(x)}\right ) \, dx\\ &=-\left (3 \int \exp \left (x-\frac {e^{-x} x \left (1-14 e^x \log (x)+3 e^x x \log (x)\right )}{\log (x)}\right ) (-5+2 x) \, dx\right )+\int \frac {\exp \left (-\frac {e^{-x} x \left (1-14 e^x \log (x)+3 e^x x \log (x)\right )}{\log (x)}\right ) (1-\log (x)+x \log (x))}{\log ^2(x)} \, dx\\ &=-\left (3 \int e^{15 x-3 x^2-\frac {e^{-x} x}{\log (x)}} (-5+2 x) \, dx\right )+\int \left (\frac {\exp \left (-\frac {e^{-x} x \left (1-14 e^x \log (x)+3 e^x x \log (x)\right )}{\log (x)}\right )}{\log ^2(x)}+\frac {\exp \left (-\frac {e^{-x} x \left (1-14 e^x \log (x)+3 e^x x \log (x)\right )}{\log (x)}\right ) (-1+x)}{\log (x)}\right ) \, dx\\ &=-\left (3 \int \left (-5 e^{15 x-3 x^2-\frac {e^{-x} x}{\log (x)}}+2 e^{15 x-3 x^2-\frac {e^{-x} x}{\log (x)}} x\right ) \, dx\right )+\int \frac {\exp \left (-\frac {e^{-x} x \left (1-14 e^x \log (x)+3 e^x x \log (x)\right )}{\log (x)}\right )}{\log ^2(x)} \, dx+\int \frac {\exp \left (-\frac {e^{-x} x \left (1-14 e^x \log (x)+3 e^x x \log (x)\right )}{\log (x)}\right ) (-1+x)}{\log (x)} \, dx\\ &=-\left (6 \int e^{15 x-3 x^2-\frac {e^{-x} x}{\log (x)}} x \, dx\right )+15 \int e^{15 x-3 x^2-\frac {e^{-x} x}{\log (x)}} \, dx+\int \frac {e^{14 x-3 x^2-\frac {e^{-x} x}{\log (x)}}}{\log ^2(x)} \, dx+\int \frac {e^{14 x-3 x^2-\frac {e^{-x} x}{\log (x)}} (-1+x)}{\log (x)} \, dx\\ &=-\left (6 \int e^{15 x-3 x^2-\frac {e^{-x} x}{\log (x)}} x \, dx\right )+15 \int e^{15 x-3 x^2-\frac {e^{-x} x}{\log (x)}} \, dx+\int \left (-\frac {e^{14 x-3 x^2-\frac {e^{-x} x}{\log (x)}}}{\log (x)}+\frac {e^{14 x-3 x^2-\frac {e^{-x} x}{\log (x)}} x}{\log (x)}\right ) \, dx+\int \frac {e^{14 x-3 x^2-\frac {e^{-x} x}{\log (x)}}}{\log ^2(x)} \, dx\\ &=-\left (6 \int e^{15 x-3 x^2-\frac {e^{-x} x}{\log (x)}} x \, dx\right )+15 \int e^{15 x-3 x^2-\frac {e^{-x} x}{\log (x)}} \, dx+\int \frac {e^{14 x-3 x^2-\frac {e^{-x} x}{\log (x)}}}{\log ^2(x)} \, dx-\int \frac {e^{14 x-3 x^2-\frac {e^{-x} x}{\log (x)}}}{\log (x)} \, dx+\int \frac {e^{14 x-3 x^2-\frac {e^{-x} x}{\log (x)}} x}{\log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.30, size = 20, normalized size = 0.87 \begin {gather*} e^{x \left (15-3 x-\frac {e^{-x}}{\log (x)}\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.20, size = 28, normalized size = 1.22
method | result | size |
risch | \({\mathrm e}^{-\frac {x \left (3 x \,{\mathrm e}^{x} \ln \left (x \right )-15 \,{\mathrm e}^{x} \ln \left (x \right )+1\right ) {\mathrm e}^{-x}}{\ln \left (x \right )}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.37, size = 21, normalized size = 0.91 \begin {gather*} e^{\left (-3 \, x^{2} + 15 \, x - \frac {x e^{\left (-x\right )}}{\log \left (x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 29, normalized size = 1.26 \begin {gather*} e^{\left (x - \frac {{\left ({\left (3 \, x^{2} - 14 \, x\right )} e^{x} \log \left (x\right ) + x\right )} e^{\left (-x\right )}}{\log \left (x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.26, size = 24, normalized size = 1.04 \begin {gather*} e^{\frac {\left (- x + \left (- 3 x^{2} + 15 x\right ) e^{x} \log {\left (x \right )}\right ) e^{- x}}{\log {\left (x \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.62, size = 23, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{15\,x}\,{\mathrm {e}}^{-3\,x^2}\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^{-x}}{\ln \left (x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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