Optimal. Leaf size=27 \[ -x^2+\frac {\log ^2(x)}{e^2 x}-6 \log \left (e^{5 x} x\right ) \]
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Rubi [A]
time = 0.03, antiderivative size = 24, normalized size of antiderivative = 0.89, number of steps
used = 8, number of rules used = 4, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 14, 2341,
2342} \begin {gather*} -x^2-30 x+\frac {\log ^2(x)}{e^2 x}-6 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2341
Rule 2342
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^2 \left (-6 x-30 x^2-2 x^3\right )+2 \log (x)-\log ^2(x)}{x^2} \, dx}{e^2}\\ &=\frac {\int \left (-\frac {2 e^2 \left (3+15 x+x^2\right )}{x}+\frac {2 \log (x)}{x^2}-\frac {\log ^2(x)}{x^2}\right ) \, dx}{e^2}\\ &=-\left (2 \int \frac {3+15 x+x^2}{x} \, dx\right )-\frac {\int \frac {\log ^2(x)}{x^2} \, dx}{e^2}+\frac {2 \int \frac {\log (x)}{x^2} \, dx}{e^2}\\ &=-\frac {2}{e^2 x}-\frac {2 \log (x)}{e^2 x}+\frac {\log ^2(x)}{e^2 x}-2 \int \left (15+\frac {3}{x}+x\right ) \, dx-\frac {2 \int \frac {\log (x)}{x^2} \, dx}{e^2}\\ &=-30 x-x^2-6 \log (x)+\frac {\log ^2(x)}{e^2 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 35, normalized size = 1.30 \begin {gather*} -\frac {30 e^2 x+e^2 x^2+6 e^2 \log (x)-\frac {\log ^2(x)}{x}}{e^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.33, size = 33, normalized size = 1.22
method | result | size |
risch | \(-x^{2}-30 x -6 \ln \left (x \right )+\frac {\ln \left (x \right )^{2} {\mathrm e}^{-2}}{x}\) | \(24\) |
norman | \(\frac {\ln \left (x \right )^{2} {\mathrm e}^{-2}-6 x \ln \left (x \right )-30 x^{2}-x^{3}}{x}\) | \(30\) |
default | \({\mathrm e}^{-2} \left (-x^{2} {\mathrm e}^{2}-30 \,{\mathrm e}^{2} x -6 \,{\mathrm e}^{2} \ln \left (x \right )+\frac {\ln \left (x \right )^{2}}{x}\right )\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 49, normalized size = 1.81 \begin {gather*} -{\left (x^{2} e^{2} + 30 \, x e^{2} + 6 \, e^{2} \log \left (x\right ) - \frac {\log \left (x\right )^{2} + 2 \, \log \left (x\right ) + 2}{x} + \frac {2 \, \log \left (x\right )}{x} + \frac {2}{x}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 33, normalized size = 1.22 \begin {gather*} -\frac {{\left (6 \, x e^{2} \log \left (x\right ) + {\left (x^{3} + 30 \, x^{2}\right )} e^{2} - \log \left (x\right )^{2}\right )} e^{\left (-2\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 20, normalized size = 0.74 \begin {gather*} - x^{2} - 30 x - 6 \log {\left (x \right )} + \frac {\log {\left (x \right )}^{2}}{x e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 34, normalized size = 1.26 \begin {gather*} -\frac {{\left (x^{3} e^{2} + 30 \, x^{2} e^{2} + 6 \, x e^{2} \log \left (x\right ) - \log \left (x\right )^{2}\right )} e^{\left (-2\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.18, size = 23, normalized size = 0.85 \begin {gather*} \frac {{\mathrm {e}}^{-2}\,{\ln \left (x\right )}^2}{x}-6\,\ln \left (x\right )-x^2-30\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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