Optimal. Leaf size=24 \[ \frac {2}{15} e^{\frac {27}{-x+\frac {\log (x)}{5 x}}} x \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(81\) vs. \(2(24)=48\).
time = 0.37, antiderivative size = 81, normalized size of antiderivative = 3.38, number of steps
used = 3, number of rules used = 3, integrand size = 69, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {6873, 12, 2326}
\begin {gather*} \frac {2 e^{-\frac {135 x}{5 x^2-\log (x)}} \left (-5 x^3+x-x \log (x)\right )}{15 \left (\frac {\left (\frac {1}{x}-10 x\right ) x}{\left (5 x^2-\log (x)\right )^2}+\frac {1}{5 x^2-\log (x)}\right ) \left (5 x^2-\log (x)\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 e^{\frac {135 x}{-5 x^2+\log (x)}} \left (-135 x+675 x^3+25 x^4+135 x \log (x)-10 x^2 \log (x)+\log ^2(x)\right )}{15 \left (5 x^2-\log (x)\right )^2} \, dx\\ &=\frac {2}{15} \int \frac {e^{\frac {135 x}{-5 x^2+\log (x)}} \left (-135 x+675 x^3+25 x^4+135 x \log (x)-10 x^2 \log (x)+\log ^2(x)\right )}{\left (5 x^2-\log (x)\right )^2} \, dx\\ &=\frac {2 e^{-\frac {135 x}{5 x^2-\log (x)}} \left (x-5 x^3-x \log (x)\right )}{15 \left (\frac {\left (\frac {1}{x}-10 x\right ) x}{\left (5 x^2-\log (x)\right )^2}+\frac {1}{5 x^2-\log (x)}\right ) \left (5 x^2-\log (x)\right )^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 20, normalized size = 0.83 \begin {gather*} \frac {2}{15} e^{\frac {135 x}{-5 x^2+\log (x)}} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 18, normalized size = 0.75
method | result | size |
risch | \(\frac {2 x \,{\mathrm e}^{\frac {135 x}{\ln \left (x \right )-5 x^{2}}}}{15}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 19, normalized size = 0.79 \begin {gather*} \frac {2}{15} \, x e^{\left (-\frac {135 \, x}{5 \, x^{2} - \log \left (x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 19, normalized size = 0.79 \begin {gather*} \frac {2}{15} \, x e^{\left (-\frac {135 \, x}{5 \, x^{2} - \log \left (x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.43, size = 17, normalized size = 0.71 \begin {gather*} \frac {2\,x\,{\mathrm {e}}^{\frac {135\,x}{\ln \left (x\right )-5\,x^2}}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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