Optimal. Leaf size=24 \[ \frac {8 e^5 \left (5+x^2\right )}{(-3+x) x^2 (1+\log (4))} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(53\) vs. \(2(24)=48\).
time = 0.18, antiderivative size = 53, normalized size of antiderivative = 2.21, number of steps
used = 6, number of rules used = 4, integrand size = 47, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.085, Rules used = {12, 1607, 6820,
1634} \begin {gather*} -\frac {40 e^5}{3 x^2 (1+\log (4))}-\frac {40 e^5}{9 x (1+\log (4))}-\frac {112 e^5}{9 (3-x) (1+\log (4))} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1607
Rule 1634
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (2 e^5\right ) \int \frac {120-60 x-4 x^3}{\left (-3 x+x^2\right ) \left (-3 x^2+x^3+\left (-3 x^2+x^3\right ) \log (4)\right )} \, dx\\ &=\left (2 e^5\right ) \int \frac {120-60 x-4 x^3}{(-3+x) x \left (-3 x^2+x^3+\left (-3 x^2+x^3\right ) \log (4)\right )} \, dx\\ &=\left (2 e^5\right ) \int \frac {4 \left (30-15 x-x^3\right )}{(3-x)^2 x^3 (1+\log (4))} \, dx\\ &=\frac {\left (8 e^5\right ) \int \frac {30-15 x-x^3}{(3-x)^2 x^3} \, dx}{1+\log (4)}\\ &=\frac {\left (8 e^5\right ) \int \left (-\frac {14}{9 (-3+x)^2}+\frac {10}{3 x^3}+\frac {5}{9 x^2}\right ) \, dx}{1+\log (4)}\\ &=-\frac {112 e^5}{9 (3-x) (1+\log (4))}-\frac {40 e^5}{3 x^2 (1+\log (4))}-\frac {40 e^5}{9 x (1+\log (4))}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 24, normalized size = 1.00 \begin {gather*} \frac {8 e^5 \left (5+x^2\right )}{(-3+x) x^2 (1+\log (4))} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(201\) vs.
\(2(29)=58\).
time = 0.29, size = 202, normalized size = 8.42
method | result | size |
risch | \(\frac {4 \,{\mathrm e}^{5} \left (2 x^{2}+10\right )}{x^{2} \left (x -3\right ) \left (1+2 \ln \left (2\right )\right )}\) | \(28\) |
gosper | \(4 \left (x^{2}+5\right ) {\mathrm e}^{\ln \left (\frac {2}{x^{2} \left (2 x \ln \left (2\right )-6 \ln \left (2\right )+x -3\right )}\right )+5}\) | \(31\) |
norman | \(\frac {\frac {8 \,{\mathrm e}^{5} x^{2}}{1+2 \ln \left (2\right )}+\frac {40 \,{\mathrm e}^{5}}{1+2 \ln \left (2\right )}}{x^{2} \left (x -3\right )}\) | \(38\) |
default | \(\frac {56 \,{\mathrm e}^{5+\ln \left (\frac {2}{2 \left (x^{3}-3 x^{2}\right ) \ln \left (2\right )+x^{3}-3 x^{2}}\right )+\ln \left (2 \left (x^{3}-3 x^{2}\right ) \ln \left (2\right )+x^{3}-3 x^{2}\right )}}{9 \left (1+2 \ln \left (2\right )\right ) \left (x -3\right )}-\frac {20 \,{\mathrm e}^{5+\ln \left (\frac {2}{2 \left (x^{3}-3 x^{2}\right ) \ln \left (2\right )+x^{3}-3 x^{2}}\right )+\ln \left (2 \left (x^{3}-3 x^{2}\right ) \ln \left (2\right )+x^{3}-3 x^{2}\right )}}{3 \left (1+2 \ln \left (2\right )\right ) x^{2}}-\frac {20 \,{\mathrm e}^{5+\ln \left (\frac {2}{2 \left (x^{3}-3 x^{2}\right ) \ln \left (2\right )+x^{3}-3 x^{2}}\right )+\ln \left (2 \left (x^{3}-3 x^{2}\right ) \ln \left (2\right )+x^{3}-3 x^{2}\right )}}{9 \left (1+2 \ln \left (2\right )\right ) x}\) | \(202\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 33, normalized size = 1.38 \begin {gather*} \frac {8 \, {\left (x^{2} + 5\right )} e^{5}}{x^{3} {\left (2 \, \log \left (2\right ) + 1\right )} - 3 \, x^{2} {\left (2 \, \log \left (2\right ) + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 33, normalized size = 1.38 \begin {gather*} \frac {8 \, {\left (x^{2} + 5\right )} e^{5}}{x^{3} - 3 \, x^{2} + 2 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.36, size = 37, normalized size = 1.54 \begin {gather*} - \frac {- 8 x^{2} e^{5} - 40 e^{5}}{x^{3} \cdot \left (1 + 2 \log {\left (2 \right )}\right ) + x^{2} \left (- 6 \log {\left (2 \right )} - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 40, normalized size = 1.67 \begin {gather*} \frac {112 \, e^{5}}{9 \, {\left (x - 3\right )} {\left (2 \, \log \left (2\right ) + 1\right )}} - \frac {40 \, {\left (x e^{5} + 3 \, e^{5}\right )}}{9 \, x^{2} {\left (2 \, \log \left (2\right ) + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.17, size = 41, normalized size = 1.71 \begin {gather*} -\frac {\frac {8\,{\mathrm {e}}^5\,x^3}{3}+40\,{\mathrm {e}}^5}{6\,x^2\,\ln \left (2\right )-2\,x^3\,\ln \left (2\right )+3\,x^2-x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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