Optimal. Leaf size=19 \[ 2-3 x-\frac {1}{\log ^2\left ((e-x) x^2\right )} \]
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Rubi [F]
time = 0.66, 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 {4 e-6 x+\left (-3 e x+3 x^2\right ) \log ^3\left (e x^2-x^3\right )}{\left (e x-x^2\right ) \log ^3\left (e x^2-x^3\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 e-6 x+\left (-3 e x+3 x^2\right ) \log ^3\left (e x^2-x^3\right )}{(e-x) x \log ^3\left (e x^2-x^3\right )} \, dx\\ &=\int \frac {4 e-6 x+\left (-3 e x+3 x^2\right ) \log ^3\left (e x^2-x^3\right )}{(e-x) x \log ^3\left ((e-x) x^2\right )} \, dx\\ &=\int \left (-3+\frac {2 (2 e-3 x)}{(e-x) x \log ^3\left ((e-x) x^2\right )}\right ) \, dx\\ &=-3 x+2 \int \frac {2 e-3 x}{(e-x) x \log ^3\left ((e-x) x^2\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 18, normalized size = 0.95 \begin {gather*} -3 x-\frac {1}{\log ^2\left ((e-x) x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.90, size = 22, normalized size = 1.16
method | result | size |
default | \(-3 x -\frac {1}{\ln \left (x^{2} {\mathrm e}-x^{3}\right )^{2}}\) | \(22\) |
risch | \(-3 x -\frac {1}{\ln \left (x^{2} {\mathrm e}-x^{3}\right )^{2}}\) | \(22\) |
norman | \(\frac {-1-3 x \ln \left (x^{2} {\mathrm e}-x^{3}\right )^{2}}{\ln \left (x^{2} {\mathrm e}-x^{3}\right )^{2}}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 64 vs.
\(2 (21) = 42\).
time = 0.29, size = 64, normalized size = 3.37 \begin {gather*} -\frac {12 \, x \log \left (x\right )^{2} + 12 \, x \log \left (x\right ) \log \left (-x + e\right ) + 3 \, x \log \left (-x + e\right )^{2} + 1}{4 \, \log \left (x\right )^{2} + 4 \, \log \left (x\right ) \log \left (-x + e\right ) + \log \left (-x + e\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 37, normalized size = 1.95 \begin {gather*} -\frac {3 \, x \log \left (-x^{3} + x^{2} e\right )^{2} + 1}{\log \left (-x^{3} + x^{2} e\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 19, normalized size = 1.00 \begin {gather*} - 3 x - \frac {1}{\log {\left (- x^{3} + e x^{2} \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.57, size = 37, normalized size = 1.95 \begin {gather*} -\frac {3 \, x \log \left (-x^{3} + x^{2} e\right )^{2} + 1}{\log \left (-x^{3} + x^{2} e\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.24, size = 21, normalized size = 1.11 \begin {gather*} -3\,x-\frac {1}{{\ln \left (x^2\,\mathrm {e}-x^3\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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