Optimal. Leaf size=20 \[ e^{\log ^2\left (30 \left (-1+e^4-x\right )^2 x^3\right )} \]
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Rubi [A]
time = 3.11, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 5, number of rules used = 6, integrand size = 111, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.054, Rules used = {6, 1607, 6820,
12, 6874, 6838} \begin {gather*} e^{\log ^2\left (30 x^3 \left (x-e^4+1\right )^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 1607
Rule 6820
Rule 6838
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\log ^2\left (30 x^3+30 e^8 x^3+60 x^4+30 x^5+e^4 \left (-60 x^3-60 x^4\right )\right )\right ) \left (-6+6 e^4-10 x\right ) \log \left (30 x^3+30 e^8 x^3+60 x^4+30 x^5+e^4 \left (-60 x^3-60 x^4\right )\right )}{\left (-1+e^4\right ) x-x^2} \, dx\\ &=\int \frac {\exp \left (\log ^2\left (30 x^3+30 e^8 x^3+60 x^4+30 x^5+e^4 \left (-60 x^3-60 x^4\right )\right )\right ) \left (-6+6 e^4-10 x\right ) \log \left (30 x^3+30 e^8 x^3+60 x^4+30 x^5+e^4 \left (-60 x^3-60 x^4\right )\right )}{\left (-1+e^4-x\right ) x} \, dx\\ &=\int \frac {2 e^{\log ^2\left (30 x^3 \left (1-e^4+x\right )^2\right )} \left (3-3 e^4+5 x\right ) \log \left (30 x^3 \left (1-e^4+x\right )^2\right )}{x \left (1-e^4+x\right )} \, dx\\ &=2 \int \frac {e^{\log ^2\left (30 x^3 \left (1-e^4+x\right )^2\right )} \left (3-3 e^4+5 x\right ) \log \left (30 x^3 \left (1-e^4+x\right )^2\right )}{x \left (1-e^4+x\right )} \, dx\\ &=e^{\log ^2\left (30 x^3 \left (1-e^4+x\right )^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 20, normalized size = 1.00 \begin {gather*} e^{\log ^2\left (30 x^3 \left (1-e^4+x\right )^2\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. \(41\) vs.
\(2(18)=36\).
time = 1.51, size = 42, normalized size = 2.10
method | result | size |
risch | \({\mathrm e}^{\ln \left (30 \,{\mathrm e}^{8} x^{3}+\left (-60 x^{4}-60 x^{3}\right ) {\mathrm e}^{4}+30 x^{5}+60 x^{4}+30 x^{3}\right )^{2}}\) | \(42\) |
norman | \({\mathrm e}^{\ln \left (30 \,{\mathrm e}^{8} x^{3}+\left (-60 x^{4}-60 x^{3}\right ) {\mathrm e}^{4}+30 x^{5}+60 x^{4}+30 x^{3}\right )^{2}}\) | \(44\) |
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. 116 vs.
\(2 (18) = 36\).
time = 0.71, size = 116, normalized size = 5.80 \begin {gather*} 3^{2 \, \log \left (5\right )} 2^{2 \, \log \left (5\right ) + 2 \, \log \left (3\right )} e^{\left (\log \left (5\right )^{2} + \log \left (3\right )^{2} + \log \left (2\right )^{2} + 4 \, \log \left (5\right ) \log \left (x - e^{4} + 1\right ) + 4 \, \log \left (3\right ) \log \left (x - e^{4} + 1\right ) + 4 \, \log \left (2\right ) \log \left (x - e^{4} + 1\right ) + 4 \, \log \left (x - e^{4} + 1\right )^{2} + 6 \, \log \left (5\right ) \log \left (x\right ) + 6 \, \log \left (3\right ) \log \left (x\right ) + 6 \, \log \left (2\right ) \log \left (x\right ) + 12 \, \log \left (x - e^{4} + 1\right ) \log \left (x\right ) + 9 \, \log \left (x\right )^{2}\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. 38 vs.
\(2 (18) = 36\).
time = 0.37, size = 38, normalized size = 1.90 \begin {gather*} e^{\left (\log \left (30 \, x^{5} + 60 \, x^{4} + 30 \, x^{3} e^{8} + 30 \, x^{3} - 60 \, {\left (x^{4} + x^{3}\right )} e^{4}\right )^{2}\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. 42 vs.
\(2 (17) = 34\).
time = 0.18, size = 42, normalized size = 2.10 \begin {gather*} e^{\log {\left (30 x^{5} + 60 x^{4} + 30 x^{3} + 30 x^{3} e^{8} + \left (- 60 x^{4} - 60 x^{3}\right ) e^{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. 41 vs.
\(2 (18) = 36\).
time = 1.60, size = 41, normalized size = 2.05 \begin {gather*} e^{\left (\log \left (30 \, x^{5} - 60 \, x^{4} e^{4} + 60 \, x^{4} + 30 \, x^{3} e^{8} - 60 \, x^{3} e^{4} + 30 \, x^{3}\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.53, size = 41, normalized size = 2.05 \begin {gather*} {\mathrm {e}}^{{\ln \left (30\,x^3\,{\mathrm {e}}^8-60\,x^4\,{\mathrm {e}}^4-60\,x^3\,{\mathrm {e}}^4+30\,x^3+60\,x^4+30\,x^5\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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