Optimal. Leaf size=22 \[ 3 e^{-\frac {5}{x^4 \log \left (x+2 x \left (-2+x^4\right )\right )}} \]
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Rubi [A]
time = 0.63, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps
used = 2, number of rules used = 2, integrand size = 70, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {1607, 6838}
\begin {gather*} 3 e^{-\frac {5}{x^4 \log \left (2 x^5-3 x\right )}} \end {gather*}
Antiderivative was successfully verified.
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Rule 1607
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-\frac {5}{x^4 \log \left (-3 x+2 x^5\right )}} \left (-45+150 x^4+\left (-180+120 x^4\right ) \log \left (-3 x+2 x^5\right )\right )}{x^5 \left (-3+2 x^4\right ) \log ^2\left (-3 x+2 x^5\right )} \, dx\\ &=3 e^{-\frac {5}{x^4 \log \left (-3 x+2 x^5\right )}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.63, size = 21, normalized size = 0.95 \begin {gather*} 3 e^{-\frac {5}{x^4 \log \left (x \left (-3+2 x^4\right )\right )}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.80, size = 21, normalized size = 0.95
method | result | size |
risch | \(3 \,{\mathrm e}^{-\frac {5}{x^{4} \ln \left (2 x^{5}-3 x \right )}}\) | \(21\) |
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 = 0.46, size = 20, normalized size = 0.91 \begin {gather*} 3 \, e^{\left (-\frac {5}{x^{4} \log \left (2 \, x^{5} - 3 \, 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 = 0.51, size = 20, normalized size = 0.91 \begin {gather*} 3 \, e^{\left (-\frac {5}{x^{4} \log \left (2 \, x^{5} - 3 \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.46, size = 20, normalized size = 0.91 \begin {gather*} 3\,{\mathrm {e}}^{-\frac {5}{x^4\,\ln \left (2\,x^5-3\,x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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