Optimal. Leaf size=26 \[ \log ^4\left (2 x+\frac {1}{2} e^e \left (-3+\frac {1}{5} (-x+\log (x))\right )\right ) \]
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Rubi [A]
time = 0.28, antiderivative size = 25, normalized size of antiderivative = 0.96, number of steps
used = 1, number of rules used = 1, integrand size = 68, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.015, Rules used = {6818}
\begin {gather*} \log ^4\left (\frac {1}{10} \left (20 x-e^e (x+15)+e^e \log (x)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6818
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log ^4\left (\frac {1}{10} \left (20 x-e^e (15+x)+e^e \log (x)\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 25, normalized size = 0.96 \begin {gather*} \log ^4\left (\frac {1}{10} \left (20 x-e^e (15+x)+e^e \log (x)\right )\right ) \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. \(111\) vs.
\(2(21)=42\).
time = 3.98, size = 112, normalized size = 4.31
method | result | size |
risch | \(\ln \left (\frac {{\mathrm e}^{{\mathrm e}} \ln \left (x \right )}{10}+\frac {\left (-x -15\right ) {\mathrm e}^{{\mathrm e}}}{10}+2 x \right )^{4}\) | \(25\) |
default | \(-4 \ln \left (10\right )^{3} \ln \left (x \,{\mathrm e}^{{\mathrm e}}-{\mathrm e}^{{\mathrm e}} \ln \left (x \right )-20 x +15 \,{\mathrm e}^{{\mathrm e}}\right )+\ln \left ({\mathrm e}^{{\mathrm e}} \ln \left (x \right )-x \,{\mathrm e}^{{\mathrm e}}-15 \,{\mathrm e}^{{\mathrm e}}+20 x \right )^{4}+6 \ln \left (10\right )^{2} \ln \left ({\mathrm e}^{{\mathrm e}} \ln \left (x \right )-x \,{\mathrm e}^{{\mathrm e}}-15 \,{\mathrm e}^{{\mathrm e}}+20 x \right )^{2}-4 \ln \left (10\right ) \ln \left ({\mathrm e}^{{\mathrm e}} \ln \left (x \right )-x \,{\mathrm e}^{{\mathrm e}}-15 \,{\mathrm e}^{{\mathrm e}}+20 x \right )^{3}\) | \(112\) |
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. 381 vs.
\(2 (19) = 38\).
time = 0.53, size = 381, normalized size = 14.65 \begin {gather*} -12 \, {\left (\log \left (5\right ) + \log \left (2\right )\right )} e \log \left (-x {\left (e^{e} - 20\right )} + e^{e} \log \left (x\right ) - 15 \, e^{e}\right )^{2} + 4 \, e \log \left (-x {\left (e^{e} - 20\right )} + e^{e} \log \left (x\right ) - 15 \, e^{e}\right )^{3} - \log \left (-x {\left (e^{e} - 20\right )} + e^{e} \log \left (x\right ) - 15 \, e^{e}\right )^{4} + 4 \, \log \left (-{\left (x {\left (e^{e} - 20\right )} - e^{e} \log \left (x\right ) + 15 \, e^{e}\right )} e^{\left (-e\right )}\right ) \log \left (-\frac {1}{10} \, {\left (x + 15\right )} e^{e} + \frac {1}{10} \, e^{e} \log \left (x\right ) + 2 \, x\right )^{3} - 6 \, {\left (\log \left (-x {\left (e^{e} - 20\right )} + e^{e} \log \left (x\right ) - 15 \, e^{e}\right )^{2} - 2 \, \log \left (-x {\left (e^{e} - 20\right )} + e^{e} \log \left (x\right ) - 15 \, e^{e}\right ) \log \left (-\frac {1}{10} \, {\left (x + 15\right )} e^{e} + \frac {1}{10} \, e^{e} \log \left (x\right ) + 2 \, x\right ) + 2 \, \log \left (-{\left (x {\left (e^{e} - 20\right )} - e^{e} \log \left (x\right ) + 15 \, e^{e}\right )} e^{\left (-e\right )}\right ) \log \left (-\frac {1}{10} \, {\left (x + 15\right )} e^{e} + \frac {1}{10} \, e^{e} \log \left (x\right ) + 2 \, x\right )\right )} \log \left (-\frac {1}{10} \, {\left (x + 15\right )} e^{e} + \frac {1}{10} \, e^{e} \log \left (x\right ) + 2 \, x\right )^{2} + 4 \, {\left (6 \, {\left (\log \left (5\right ) + \log \left (2\right )\right )} e \log \left (-x {\left (e^{e} - 20\right )} + e^{e} \log \left (x\right ) - 15 \, e^{e}\right ) - 3 \, e \log \left (-x {\left (e^{e} - 20\right )} + e^{e} \log \left (x\right ) - 15 \, e^{e}\right )^{2} + \log \left (-x {\left (e^{e} - 20\right )} + e^{e} \log \left (x\right ) - 15 \, e^{e}\right )^{3}\right )} \log \left (-\frac {1}{10} \, {\left (x + 15\right )} e^{e} + \frac {1}{10} \, e^{e} \log \left (x\right ) + 2 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 22, normalized size = 0.85 \begin {gather*} \log \left (-\frac {1}{10} \, {\left (x + 15\right )} e^{e} + \frac {1}{10} \, e^{e} \log \left (x\right ) + 2 \, x\right )^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 29, normalized size = 1.12 \begin {gather*} \log {\left (2 x + \left (- \frac {x}{10} - \frac {3}{2}\right ) e^{e} + \frac {e^{e} \log {\left (x \right )}}{10} \right )}^{4} \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. 111 vs.
\(2 (19) = 38\).
time = 0.69, size = 111, normalized size = 4.27 \begin {gather*} -4 \, \log \left (10\right )^{3} \log \left (-x e^{e} + e^{e} \log \left (x\right ) + 20 \, x - 15 \, e^{e}\right ) + 6 \, \log \left (10\right )^{2} \log \left (-x e^{e} + e^{e} \log \left (x\right ) + 20 \, x - 15 \, e^{e}\right )^{2} - 4 \, \log \left (10\right ) \log \left (-x e^{e} + e^{e} \log \left (x\right ) + 20 \, x - 15 \, e^{e}\right )^{3} + \log \left (-x e^{e} + e^{e} \log \left (x\right ) + 20 \, x - 15 \, e^{e}\right )^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.27, size = 22, normalized size = 0.85 \begin {gather*} {\ln \left (2\,x-\frac {{\mathrm {e}}^{\mathrm {e}}\,\left (x+15\right )}{10}+\frac {{\mathrm {e}}^{\mathrm {e}}\,\ln \left (x\right )}{10}\right )}^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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