Optimal. Leaf size=26 \[ \frac {x^3 \left (e^3+x\right ) \log \left (\frac {-1+e^4}{12 x}\right )}{\log (4)} \]
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Rubi [A]
time = 0.04, antiderivative size = 31, normalized size of antiderivative = 1.19, 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, 45,
2371} \begin {gather*} \frac {\left (x^4+e^3 x^3\right ) \log \left (-\frac {1-e^4}{12 x}\right )}{\log (4)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 45
Rule 1607
Rule 2371
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-e^3 x^2-x^3+\left (3 e^3 x^2+4 x^3\right ) \log \left (\frac {-1+e^4}{12 x}\right )\right ) \, dx}{\log (4)}\\ &=-\frac {e^3 x^3}{3 \log (4)}-\frac {x^4}{4 \log (4)}+\frac {\int \left (3 e^3 x^2+4 x^3\right ) \log \left (\frac {-1+e^4}{12 x}\right ) \, dx}{\log (4)}\\ &=-\frac {e^3 x^3}{3 \log (4)}-\frac {x^4}{4 \log (4)}+\frac {\int x^2 \left (3 e^3+4 x\right ) \log \left (\frac {-1+e^4}{12 x}\right ) \, dx}{\log (4)}\\ &=-\frac {e^3 x^3}{3 \log (4)}-\frac {x^4}{4 \log (4)}+\frac {\left (e^3 x^3+x^4\right ) \log \left (-\frac {1-e^4}{12 x}\right )}{\log (4)}+\frac {\int x^2 \left (e^3+x\right ) \, dx}{\log (4)}\\ &=-\frac {e^3 x^3}{3 \log (4)}-\frac {x^4}{4 \log (4)}+\frac {\left (e^3 x^3+x^4\right ) \log \left (-\frac {1-e^4}{12 x}\right )}{\log (4)}+\frac {\int \left (e^3 x^2+x^3\right ) \, dx}{\log (4)}\\ &=\frac {\left (e^3 x^3+x^4\right ) \log \left (-\frac {1-e^4}{12 x}\right )}{\log (4)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 45, normalized size = 1.73 \begin {gather*} \frac {e^3 x^3 \log \left (-\frac {1-e^4}{12 x}\right )+x^4 \log \left (\frac {-1+e^4}{12 x}\right )}{\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. \(416\) vs.
\(2(23)=46\).
time = 0.98, size = 417, normalized size = 16.04 Too large to display
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.36, size = 26, normalized size = 1.00 \begin {gather*} \frac {{\left (x^{4} + x^{3} e^{3}\right )} \log \left (\frac {e^{4} - 1}{12 \, x}\right )}{2 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 26, normalized size = 1.00 \begin {gather*} \frac {{\left (x^{4} + x^{3} e^{3}\right )} \log \left (\frac {e^{4} - 1}{12 \, x}\right )}{2 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 26, normalized size = 1.00 \begin {gather*} \frac {\left (x^{4} + x^{3} e^{3}\right ) \log {\left (\frac {- \frac {1}{12} + \frac {e^{4}}{12}}{x} \right )}}{2 \log {\left (2 \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. 209 vs.
\(2 (23) = 46\).
time = 0.40, size = 209, normalized size = 8.04 \begin {gather*} -\frac {3 \, x^{4} + 4 \, x^{3} e^{3} - \frac {\frac {12 \, x^{4} {\left (\frac {{\left (e^{4} - 1\right )} e^{19}}{x} - \frac {4 \, {\left (e^{4} - 1\right )} e^{15}}{x} + \frac {6 \, {\left (e^{4} - 1\right )} e^{11}}{x} - \frac {4 \, {\left (e^{4} - 1\right )} e^{7}}{x} + \frac {{\left (e^{4} - 1\right )} e^{3}}{x} + e^{20} - 5 \, e^{16} + 10 \, e^{12} - 10 \, e^{8} + 5 \, e^{4} - 1\right )} \log \left (\frac {e^{4} - 1}{12 \, x}\right )}{{\left (e^{4} - 1\right )}^{4}} + \frac {x^{4} {\left (\frac {4 \, {\left (e^{4} - 1\right )} e^{19}}{x} - \frac {16 \, {\left (e^{4} - 1\right )} e^{15}}{x} + \frac {24 \, {\left (e^{4} - 1\right )} e^{11}}{x} - \frac {16 \, {\left (e^{4} - 1\right )} e^{7}}{x} + \frac {4 \, {\left (e^{4} - 1\right )} e^{3}}{x} + 3 \, e^{20} - 15 \, e^{16} + 30 \, e^{12} - 30 \, e^{8} + 15 \, e^{4} - 3\right )}}{{\left (e^{4} - 1\right )}^{4}}}{e^{4} - 1}}{24 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.65, size = 25, normalized size = 0.96 \begin {gather*} \frac {x^3\,\left (\ln \left (\frac {1}{x}\right )+\ln \left (\frac {{\mathrm {e}}^4}{12}-\frac {1}{12}\right )\right )\,\left (x+{\mathrm {e}}^3\right )}{2\,\ln \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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