Optimal. Leaf size=22 \[ \log ^2(30)+\left (-2+(3-3 x) x+e^5 \log (x)\right )^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(80\) vs. \(2(22)=44\).
time = 0.07, antiderivative size = 80, normalized size of antiderivative = 3.64, number of steps
used = 9, number of rules used = 5, integrand size = 59, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.085, Rules used = {14, 2404, 2332,
2338, 2341} \begin {gather*} 9 x^4-18 x^3+3 \left (7-e^5\right ) x^2+3 e^5 x^2-6 e^5 x^2 \log (x)-6 \left (2-e^5\right ) x-6 e^5 x+e^{10} \log ^2(x)+6 e^5 x \log (x)-4 e^5 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2332
Rule 2338
Rule 2341
Rule 2404
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 \left (-2 e^5-3 \left (2-e^5\right ) x+3 \left (7-e^5\right ) x^2-27 x^3+18 x^4\right )}{x}+\frac {2 e^5 \left (e^5+3 x-6 x^2\right ) \log (x)}{x}\right ) \, dx\\ &=2 \int \frac {-2 e^5-3 \left (2-e^5\right ) x+3 \left (7-e^5\right ) x^2-27 x^3+18 x^4}{x} \, dx+\left (2 e^5\right ) \int \frac {\left (e^5+3 x-6 x^2\right ) \log (x)}{x} \, dx\\ &=2 \int \left (-3 \left (2-e^5\right )-\frac {2 e^5}{x}+3 \left (7-e^5\right ) x-27 x^2+18 x^3\right ) \, dx+\left (2 e^5\right ) \int \left (3 \log (x)+\frac {e^5 \log (x)}{x}-6 x \log (x)\right ) \, dx\\ &=-6 \left (2-e^5\right ) x+3 \left (7-e^5\right ) x^2-18 x^3+9 x^4-4 e^5 \log (x)+\left (6 e^5\right ) \int \log (x) \, dx-\left (12 e^5\right ) \int x \log (x) \, dx+\left (2 e^{10}\right ) \int \frac {\log (x)}{x} \, dx\\ &=-6 e^5 x-6 \left (2-e^5\right ) x+3 e^5 x^2+3 \left (7-e^5\right ) x^2-18 x^3+9 x^4-4 e^5 \log (x)+6 e^5 x \log (x)-6 e^5 x^2 \log (x)+e^{10} \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(52\) vs. \(2(22)=44\).
time = 0.01, size = 52, normalized size = 2.36 \begin {gather*} -12 x+21 x^2-18 x^3+9 x^4-4 e^5 \log (x)+6 e^5 x \log (x)-6 e^5 x^2 \log (x)+e^{10} \log ^2(x) \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. \(75\) vs.
\(2(21)=42\).
time = 0.10, size = 76, normalized size = 3.45
method | result | size |
risch | \({\mathrm e}^{10} \ln \left (x \right )^{2}-6 \,{\mathrm e}^{5} x \left (x -1\right ) \ln \left (x \right )+9 x^{4}-18 x^{3}-4 \,{\mathrm e}^{5} \ln \left (x \right )+21 x^{2}-12 x +4\) | \(44\) |
norman | \(-4 \,{\mathrm e}^{5} \ln \left (x \right )+{\mathrm e}^{10} \ln \left (x \right )^{2}-12 x +21 x^{2}-18 x^{3}+9 x^{4}+6 x \,{\mathrm e}^{5} \ln \left (x \right )-6 x^{2} {\mathrm e}^{5} \ln \left (x \right )\) | \(51\) |
default | \(-12 \,{\mathrm e}^{5} \left (\frac {x^{2} \ln \left (x \right )}{2}-\frac {x^{2}}{4}\right )+9 x^{4}+{\mathrm e}^{10} \ln \left (x \right )^{2}+6 \,{\mathrm e}^{5} \left (x \ln \left (x \right )-x \right )-3 x^{2} {\mathrm e}^{5}-18 x^{3}+6 x \,{\mathrm e}^{5}+21 x^{2}-4 \,{\mathrm e}^{5} \ln \left (x \right )-12 x\) | \(76\) |
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. 73 vs.
\(2 (21) = 42\).
time = 0.27, size = 73, normalized size = 3.32 \begin {gather*} 9 \, x^{4} - 18 \, x^{3} - 3 \, x^{2} e^{5} + e^{10} \log \left (x\right )^{2} + 21 \, x^{2} - 3 \, {\left (2 \, x^{2} \log \left (x\right ) - x^{2}\right )} e^{5} + 6 \, {\left (x \log \left (x\right ) - x\right )} e^{5} + 6 \, x e^{5} - 4 \, e^{5} \log \left (x\right ) - 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 42, normalized size = 1.91 \begin {gather*} 9 \, x^{4} - 18 \, x^{3} - 2 \, {\left (3 \, x^{2} - 3 \, x + 2\right )} e^{5} \log \left (x\right ) + e^{10} \log \left (x\right )^{2} + 21 \, x^{2} - 12 \, x \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. 53 vs.
\(2 (20) = 40\).
time = 0.09, size = 53, normalized size = 2.41 \begin {gather*} 9 x^{4} - 18 x^{3} + 21 x^{2} - 12 x + \left (- 6 x^{2} e^{5} + 6 x e^{5}\right ) \log {\left (x \right )} + e^{10} \log {\left (x \right )}^{2} - 4 e^{5} \log {\left (x \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. 48 vs.
\(2 (21) = 42\).
time = 0.44, size = 48, normalized size = 2.18 \begin {gather*} 9 \, x^{4} - 6 \, x^{2} e^{5} \log \left (x\right ) - 18 \, x^{3} + 6 \, x e^{5} \log \left (x\right ) + e^{10} \log \left (x\right )^{2} + 21 \, x^{2} - 4 \, e^{5} \log \left (x\right ) - 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.56, size = 48, normalized size = 2.18 \begin {gather*} 9\,x^4-18\,x^3-6\,{\mathrm {e}}^5\,x^2\,\ln \left (x\right )+21\,x^2+6\,{\mathrm {e}}^5\,x\,\ln \left (x\right )-12\,x+{\mathrm {e}}^{10}\,{\ln \left (x\right )}^2-4\,{\mathrm {e}}^5\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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