Optimal. Leaf size=22 \[ \log \left (e^{e^{(x+x \log (x))^4}}+3 x-x^3\right ) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(52\) vs. \(2(22)=44\).
time = 0.36, antiderivative size = 52, normalized size of antiderivative = 2.36, number of steps
used = 1, number of rules used = 1, integrand size = 179, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {6816}
\begin {gather*} \log \left (\exp \left (x^{4 x^4} \exp \left (x^4+x^4 \log ^4(x)+4 x^4 \log ^3(x)+6 x^4 \log ^2(x)\right )\right )-x^3+3 x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (\exp \left (\exp \left (x^4+6 x^4 \log ^2(x)+4 x^4 \log ^3(x)+x^4 \log ^4(x)\right ) x^{4 x^4}\right )+3 x-x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(51\) vs. \(2(22)=44\).
time = 0.36, size = 51, normalized size = 2.32 \begin {gather*} \log \left (e^{e^{x^4+4 x^4 \log (x)+6 x^4 \log ^2(x)+4 x^4 \log ^3(x)+x^4 \log ^4(x)}}+3 x-x^3\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. \(49\) vs.
\(2(20)=40\).
time = 0.07, size = 50, normalized size = 2.27
method | result | size |
risch | \(\ln \left ({\mathrm e}^{x^{4 x^{4}} {\mathrm e}^{x^{4} \left (\ln \left (x \right )^{4}+4 \ln \left (x \right )^{3}+6 \ln \left (x \right )^{2}+1\right )}}-x^{3}+3 x \right )\) | \(43\) |
derivativedivides | \(\ln \left ({\mathrm e}^{{\mathrm e}^{x^{4} \ln \left (x \right )^{4}+4 x^{4} \ln \left (x \right )^{3}+6 x^{4} \ln \left (x \right )^{2}+4 x^{4} \ln \left (x \right )+x^{4}}}-x^{3}+3 x \right )\) | \(50\) |
default | \(\ln \left ({\mathrm e}^{{\mathrm e}^{x^{4} \ln \left (x \right )^{4}+4 x^{4} \ln \left (x \right )^{3}+6 x^{4} \ln \left (x \right )^{2}+4 x^{4} \ln \left (x \right )+x^{4}}}-x^{3}+3 x \right )\) | \(50\) |
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. 49 vs.
\(2 (20) = 40\).
time = 0.31, size = 49, normalized size = 2.23 \begin {gather*} \log \left (-x^{3} + 3 \, x + e^{\left (e^{\left (x^{4} \log \left (x\right )^{4} + 4 \, x^{4} \log \left (x\right )^{3} + 6 \, x^{4} \log \left (x\right )^{2} + 4 \, x^{4} \log \left (x\right ) + x^{4}\right )}\right )}\right ) \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. 165 vs.
\(2 (20) = 40\).
time = 0.45, size = 165, normalized size = 7.50 \begin {gather*} -x^{4} \log \left (x\right )^{4} - 4 \, x^{4} \log \left (x\right )^{3} - 6 \, x^{4} \log \left (x\right )^{2} - 4 \, x^{4} \log \left (x\right ) - x^{4} + \log \left (-{\left (x^{3} - 3 \, x\right )} e^{\left (x^{4} \log \left (x\right )^{4} + 4 \, x^{4} \log \left (x\right )^{3} + 6 \, x^{4} \log \left (x\right )^{2} + 4 \, x^{4} \log \left (x\right ) + x^{4}\right )} + e^{\left (x^{4} \log \left (x\right )^{4} + 4 \, x^{4} \log \left (x\right )^{3} + 6 \, x^{4} \log \left (x\right )^{2} + 4 \, x^{4} \log \left (x\right ) + x^{4} + e^{\left (x^{4} \log \left (x\right )^{4} + 4 \, x^{4} \log \left (x\right )^{3} + 6 \, x^{4} \log \left (x\right )^{2} + 4 \, x^{4} \log \left (x\right ) + x^{4}\right )}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 51 vs.
\(2 (19) = 38\).
time = 0.44, size = 51, normalized size = 2.32 \begin {gather*} \log {\left (- x^{3} + 3 x + e^{e^{x^{4} \log {\left (x \right )}^{4} + 4 x^{4} \log {\left (x \right )}^{3} + 6 x^{4} \log {\left (x \right )}^{2} + 4 x^{4} \log {\left (x \right )} + x^{4}}} \right )} \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. 202 vs.
\(2 (20) = 40\).
time = 2.15, size = 202, normalized size = 9.18 \begin {gather*} -x^{4} \log \left (x\right )^{4} - 4 \, x^{4} \log \left (x\right )^{3} - 6 \, x^{4} \log \left (x\right )^{2} - 4 \, x^{4} \log \left (x\right ) - x^{4} + \log \left (-x^{3} e^{\left (x^{4} \log \left (x\right )^{4} + 4 \, x^{4} \log \left (x\right )^{3} + 6 \, x^{4} \log \left (x\right )^{2} + 4 \, x^{4} \log \left (x\right ) + x^{4}\right )} + 3 \, x e^{\left (x^{4} \log \left (x\right )^{4} + 4 \, x^{4} \log \left (x\right )^{3} + 6 \, x^{4} \log \left (x\right )^{2} + 4 \, x^{4} \log \left (x\right ) + x^{4}\right )} + e^{\left (x^{4} \log \left (x\right )^{4} + 4 \, x^{4} \log \left (x\right )^{3} + 6 \, x^{4} \log \left (x\right )^{2} + 4 \, x^{4} \log \left (x\right ) + x^{4} + e^{\left (x^{4} \log \left (x\right )^{4} + 4 \, x^{4} \log \left (x\right )^{3} + 6 \, x^{4} \log \left (x\right )^{2} + 4 \, x^{4} \log \left (x\right ) + x^{4}\right )}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.95, size = 52, normalized size = 2.36 \begin {gather*} \ln \left (3\,x+{\mathrm {e}}^{x^{4\,x^4}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{x^4\,{\ln \left (x\right )}^4}\,{\mathrm {e}}^{4\,x^4\,{\ln \left (x\right )}^3}\,{\mathrm {e}}^{6\,x^4\,{\ln \left (x\right )}^2}}-x^3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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