Optimal. Leaf size=29 \[ -x+e^{\frac {5 \left (3+\frac {1}{10 x}\right )}{x}} \left (x+\frac {x}{\log (x)}\right ) \]
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Rubi [A]
time = 1.15, antiderivative size = 57, normalized size of antiderivative = 1.97, number of steps
used = 3, number of rules used = 2, integrand size = 87, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6874, 2326}
\begin {gather*} \frac {e^{\frac {1}{2 x^2}+\frac {15}{x}} \left (15 x \log ^2(x)+\log ^2(x)+15 x \log (x)+\log (x)\right )}{\left (\frac {1}{x^3}+\frac {15}{x^2}\right ) x^2 \log ^2(x)}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+\frac {e^{\frac {1}{2 x^2}+\frac {15}{x}} \left (-x^2-\log (x)-15 x \log (x)+x^2 \log (x)-\log ^2(x)-15 x \log ^2(x)+x^2 \log ^2(x)\right )}{x^2 \log ^2(x)}\right ) \, dx\\ &=-x+\int \frac {e^{\frac {1}{2 x^2}+\frac {15}{x}} \left (-x^2-\log (x)-15 x \log (x)+x^2 \log (x)-\log ^2(x)-15 x \log ^2(x)+x^2 \log ^2(x)\right )}{x^2 \log ^2(x)} \, dx\\ &=-x+\frac {e^{\frac {1}{2 x^2}+\frac {15}{x}} \left (\log (x)+15 x \log (x)+\log ^2(x)+15 x \log ^2(x)\right )}{\left (\frac {1}{x^3}+\frac {15}{x^2}\right ) x^2 \log ^2(x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.12, size = 39, normalized size = 1.34 \begin {gather*} \left (-1+e^{\frac {1+30 x}{2 x^2}}\right ) x+\frac {e^{\frac {1+30 x}{2 x^2}} x}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.22, size = 46, normalized size = 1.59
method | result | size |
risch | \(x \,{\mathrm e}^{\frac {30 x +1}{2 x^{2}}}-x +\frac {x \,{\mathrm e}^{\frac {30 x +1}{2 x^{2}}}}{\ln \left (x \right )}\) | \(35\) |
default | \(-x +\frac {x^{2} {\mathrm e}^{\frac {30 x +1}{2 x^{2}}}+{\mathrm e}^{\frac {30 x +1}{2 x^{2}}} \ln \left (x \right ) x^{2}}{\ln \left (x \right ) x}\) | \(46\) |
norman | \(\frac {x^{2} {\mathrm e}^{\frac {30 x +1}{2 x^{2}}}+{\mathrm e}^{\frac {30 x +1}{2 x^{2}}} \ln \left (x \right ) x^{2}-x^{2} \ln \left (x \right )}{x \ln \left (x \right )}\) | \(49\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 27, normalized size = 0.93 \begin {gather*} -x + \frac {{\left (x \log \left (x\right ) + x\right )} e^{\left (\frac {15}{x} + \frac {1}{2 \, x^{2}}\right )}}{\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 39, normalized size = 1.34 \begin {gather*} \frac {x e^{\left (\frac {30 \, x + 1}{2 \, x^{2}}\right )} + {\left (x e^{\left (\frac {30 \, x + 1}{2 \, x^{2}}\right )} - x\right )} \log \left (x\right )}{\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 22, normalized size = 0.76 \begin {gather*} - x + \frac {\left (x \log {\left (x \right )} + x\right ) e^{\frac {15 x + \frac {1}{2}}{x^{2}}}}{\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 [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {x^2\,{\mathrm {e}}^{\frac {15\,x+\frac {1}{2}}{x^2}}+{\ln \left (x\right )}^2\,\left ({\mathrm {e}}^{\frac {15\,x+\frac {1}{2}}{x^2}}\,\left (-x^2+15\,x+1\right )+x^2\right )+{\mathrm {e}}^{\frac {15\,x+\frac {1}{2}}{x^2}}\,\ln \left (x\right )\,\left (-x^2+15\,x+1\right )}{x^2\,{\ln \left (x\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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