Optimal. Leaf size=26 \[ 5 e^{5 x}+\frac {2}{\left (x+\frac {1}{25} \log \left (-4+3 x^6\right )\right )^2} \]
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Rubi [F]
time = 4.88, 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 {250000-45000 x^5-187500 x^6+e^{5 x} \left (-1562500 x^3+1171875 x^9\right )+e^{5 x} \left (-187500 x^2+140625 x^8\right ) \log \left (-4+3 x^6\right )+e^{5 x} \left (-7500 x+5625 x^7\right ) \log ^2\left (-4+3 x^6\right )+e^{5 x} \left (-100+75 x^6\right ) \log ^3\left (-4+3 x^6\right )}{-62500 x^3+46875 x^9+\left (-7500 x^2+5625 x^8\right ) \log \left (-4+3 x^6\right )+\left (-300 x+225 x^7\right ) \log ^2\left (-4+3 x^6\right )+\left (-4+3 x^6\right ) \log ^3\left (-4+3 x^6\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 {-250000+45000 x^5+187500 x^6-e^{5 x} \left (-1562500 x^3+1171875 x^9\right )-e^{5 x} \left (-187500 x^2+140625 x^8\right ) \log \left (-4+3 x^6\right )-e^{5 x} \left (-7500 x+5625 x^7\right ) \log ^2\left (-4+3 x^6\right )-e^{5 x} \left (-100+75 x^6\right ) \log ^3\left (-4+3 x^6\right )}{\left (4-3 x^6\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3} \, dx\\ &=\int \left (25 e^{5 x}+\frac {250000}{\left (-4+3 x^6\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}-\frac {45000 x^5}{\left (-4+3 x^6\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}-\frac {187500 x^6}{\left (-4+3 x^6\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}\right ) \, dx\\ &=25 \int e^{5 x} \, dx-45000 \int \frac {x^5}{\left (-4+3 x^6\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3} \, dx-187500 \int \frac {x^6}{\left (-4+3 x^6\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3} \, dx+250000 \int \frac {1}{\left (-4+3 x^6\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3} \, dx\\ &=5 e^{5 x}-45000 \int \left (\frac {x^2}{2 \left (-2 \sqrt {3}+3 x^3\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}+\frac {x^2}{2 \left (2 \sqrt {3}+3 x^3\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}\right ) \, dx-187500 \int \left (\frac {1}{3 \left (25 x+\log \left (-4+3 x^6\right )\right )^3}+\frac {4}{3 \left (-4+3 x^6\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}\right ) \, dx+250000 \int \left (-\frac {1}{4 \left (2-\sqrt {3} x^3\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}-\frac {1}{4 \left (2+\sqrt {3} x^3\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}\right ) \, dx\\ &=5 e^{5 x}-22500 \int \frac {x^2}{\left (-2 \sqrt {3}+3 x^3\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3} \, dx-22500 \int \frac {x^2}{\left (2 \sqrt {3}+3 x^3\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3} \, dx-62500 \int \frac {1}{\left (25 x+\log \left (-4+3 x^6\right )\right )^3} \, dx-62500 \int \frac {1}{\left (2-\sqrt {3} x^3\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3} \, dx-62500 \int \frac {1}{\left (2+\sqrt {3} x^3\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3} \, dx-250000 \int \frac {1}{\left (-4+3 x^6\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3} \, dx\\ &=5 e^{5 x}-22500 \int \left (-\frac {1}{3\ 3^{5/6} \left (-\sqrt [3]{-2}-\sqrt [6]{3} x\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}-\frac {1}{3\ 3^{5/6} \left (\sqrt [3]{2}-\sqrt [6]{3} x\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}-\frac {1}{3\ 3^{5/6} \left ((-1)^{2/3} \sqrt [3]{2}-\sqrt [6]{3} x\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}\right ) \, dx-22500 \int \left (\frac {1}{3\ 3^{5/6} \left (-\sqrt [3]{-2}+\sqrt [6]{3} x\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}+\frac {1}{3\ 3^{5/6} \left (\sqrt [3]{2}+\sqrt [6]{3} x\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}+\frac {1}{3\ 3^{5/6} \left ((-1)^{2/3} \sqrt [3]{2}+\sqrt [6]{3} x\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}\right ) \, dx-62500 \int \frac {1}{\left (25 x+\log \left (-4+3 x^6\right )\right )^3} \, dx-62500 \int \left (-\frac {1}{3\ 2^{2/3} \left (-\sqrt [3]{2}-\sqrt [6]{3} x\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}-\frac {1}{3\ 2^{2/3} \left (-\sqrt [3]{2}+\sqrt [3]{-1} \sqrt [6]{3} x\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}-\frac {1}{3\ 2^{2/3} \left (-\sqrt [3]{2}-(-1)^{2/3} \sqrt [6]{3} x\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}\right ) \, dx-62500 \int \left (\frac {1}{3\ 2^{2/3} \left (\sqrt [3]{2}-\sqrt [6]{3} x\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}+\frac {1}{3\ 2^{2/3} \left (\sqrt [3]{2}+\sqrt [3]{-1} \sqrt [6]{3} x\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}+\frac {1}{3\ 2^{2/3} \left (\sqrt [3]{2}-(-1)^{2/3} \sqrt [6]{3} x\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}\right ) \, dx-250000 \int \left (-\frac {1}{4 \left (2-\sqrt {3} x^3\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}-\frac {1}{4 \left (2+\sqrt {3} x^3\right ) \left (25 x+\log \left (-4+3 x^6\right )\right )^3}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 28, normalized size = 1.08 \begin {gather*} 25 \left (\frac {e^{5 x}}{5}+\frac {50}{\left (25 x+\log \left (-4+3 x^6\right )\right )^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.82, size = 24, normalized size = 0.92
method | result | size |
risch | \(5 \,{\mathrm e}^{5 x}+\frac {1250}{\left (\ln \left (3 x^{6}-4\right )+25 x \right )^{2}}\) | \(24\) |
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. 72 vs.
\(2 (23) = 46\).
time = 0.67, size = 72, normalized size = 2.77 \begin {gather*} \frac {5 \, {\left (625 \, x^{2} e^{\left (5 \, x\right )} + 50 \, x e^{\left (5 \, x\right )} \log \left (3 \, x^{6} - 4\right ) + e^{\left (5 \, x\right )} \log \left (3 \, x^{6} - 4\right )^{2} + 250\right )}}{625 \, x^{2} + 50 \, x \log \left (3 \, x^{6} - 4\right ) + \log \left (3 \, x^{6} - 4\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 72 vs.
\(2 (23) = 46\).
time = 0.35, size = 72, normalized size = 2.77 \begin {gather*} \frac {5 \, {\left (625 \, x^{2} e^{\left (5 \, x\right )} + 50 \, x e^{\left (5 \, x\right )} \log \left (3 \, x^{6} - 4\right ) + e^{\left (5 \, x\right )} \log \left (3 \, x^{6} - 4\right )^{2} + 250\right )}}{625 \, x^{2} + 50 \, x \log \left (3 \, x^{6} - 4\right ) + \log \left (3 \, x^{6} - 4\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 34, normalized size = 1.31 \begin {gather*} 5 e^{5 x} + \frac {1250}{625 x^{2} + 50 x \log {\left (3 x^{6} - 4 \right )} + \log {\left (3 x^{6} - 4 \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 72 vs.
\(2 (23) = 46\).
time = 3.58, size = 72, normalized size = 2.77 \begin {gather*} \frac {5 \, {\left (625 \, x^{2} e^{\left (5 \, x\right )} + 50 \, x e^{\left (5 \, x\right )} \log \left (3 \, x^{6} - 4\right ) + e^{\left (5 \, x\right )} \log \left (3 \, x^{6} - 4\right )^{2} + 250\right )}}{625 \, x^{2} + 50 \, x \log \left (3 \, x^{6} - 4\right ) + \log \left (3 \, x^{6} - 4\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.17, size = 23, normalized size = 0.88 \begin {gather*} 5\,{\mathrm {e}}^{5\,x}+\frac {1250}{{\left (25\,x+\ln \left (3\,x^6-4\right )\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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