Optimal. Leaf size=31 \[ \frac {e^{25-x}}{5}-\frac {x+\frac {1}{2} \log (x) \log ^2\left (x^2\right )}{x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(104\) vs. \(2(31)=62\).
time = 0.18, antiderivative size = 104, normalized size of antiderivative = 3.35, number of steps
used = 14, number of rules used = 8, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.195, Rules used = {12, 14, 2225,
2341, 2340, 2413, 6874, 2342} \begin {gather*} \frac {(1-\log (x)) \log ^2\left (x^2\right )}{2 x}-\frac {\log ^2\left (x^2\right )}{2 x}+\frac {2 (1-\log (x)) \log \left (x^2\right )}{x}+\frac {2 \log (x) \log \left (x^2\right )}{x}-\frac {2 \log \left (x^2\right )}{x}+\frac {e^{25-x}}{5}-\frac {8}{x}+\frac {4 (1-\log (x))}{x}+\frac {4 (\log (x)+1)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2225
Rule 2340
Rule 2341
Rule 2342
Rule 2413
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{10} \int \frac {-2 e^{25-x} x^2-20 \log (x) \log \left (x^2\right )+(-5+5 \log (x)) \log ^2\left (x^2\right )}{x^2} \, dx\\ &=\frac {1}{10} \int \left (-2 e^{25-x}+\frac {5 \log \left (x^2\right ) \left (-4 \log (x)-\log \left (x^2\right )+\log (x) \log \left (x^2\right )\right )}{x^2}\right ) \, dx\\ &=-\left (\frac {1}{5} \int e^{25-x} \, dx\right )+\frac {1}{2} \int \frac {\log \left (x^2\right ) \left (-4 \log (x)-\log \left (x^2\right )+\log (x) \log \left (x^2\right )\right )}{x^2} \, dx\\ &=\frac {e^{25-x}}{5}+\frac {1}{2} \int \left (-\frac {4 \log (x) \log \left (x^2\right )}{x^2}+\frac {(-1+\log (x)) \log ^2\left (x^2\right )}{x^2}\right ) \, dx\\ &=\frac {e^{25-x}}{5}+\frac {1}{2} \int \frac {(-1+\log (x)) \log ^2\left (x^2\right )}{x^2} \, dx-2 \int \frac {\log (x) \log \left (x^2\right )}{x^2} \, dx\\ &=\frac {e^{25-x}}{5}+\frac {4 (1-\log (x))}{x}+\frac {2 \log \left (x^2\right )}{x}+\frac {2 (1-\log (x)) \log \left (x^2\right )}{x}+\frac {2 \log (x) \log \left (x^2\right )}{x}+\frac {(1-\log (x)) \log ^2\left (x^2\right )}{2 x}-\frac {1}{2} \int \frac {-8-4 \log \left (x^2\right )-\log ^2\left (x^2\right )}{x^2} \, dx+4 \int \frac {-1-\log (x)}{x^2} \, dx\\ &=\frac {e^{25-x}}{5}+\frac {4}{x}+\frac {4 (1-\log (x))}{x}+\frac {4 (1+\log (x))}{x}+\frac {2 \log \left (x^2\right )}{x}+\frac {2 (1-\log (x)) \log \left (x^2\right )}{x}+\frac {2 \log (x) \log \left (x^2\right )}{x}+\frac {(1-\log (x)) \log ^2\left (x^2\right )}{2 x}-\frac {1}{2} \int \left (-\frac {8}{x^2}-\frac {4 \log \left (x^2\right )}{x^2}-\frac {\log ^2\left (x^2\right )}{x^2}\right ) \, dx\\ &=\frac {e^{25-x}}{5}+\frac {4 (1-\log (x))}{x}+\frac {4 (1+\log (x))}{x}+\frac {2 \log \left (x^2\right )}{x}+\frac {2 (1-\log (x)) \log \left (x^2\right )}{x}+\frac {2 \log (x) \log \left (x^2\right )}{x}+\frac {(1-\log (x)) \log ^2\left (x^2\right )}{2 x}+\frac {1}{2} \int \frac {\log ^2\left (x^2\right )}{x^2} \, dx+2 \int \frac {\log \left (x^2\right )}{x^2} \, dx\\ &=\frac {e^{25-x}}{5}-\frac {4}{x}+\frac {4 (1-\log (x))}{x}+\frac {4 (1+\log (x))}{x}+\frac {2 (1-\log (x)) \log \left (x^2\right )}{x}+\frac {2 \log (x) \log \left (x^2\right )}{x}-\frac {\log ^2\left (x^2\right )}{2 x}+\frac {(1-\log (x)) \log ^2\left (x^2\right )}{2 x}+2 \int \frac {\log \left (x^2\right )}{x^2} \, dx\\ &=\frac {e^{25-x}}{5}-\frac {8}{x}+\frac {4 (1-\log (x))}{x}+\frac {4 (1+\log (x))}{x}-\frac {2 \log \left (x^2\right )}{x}+\frac {2 (1-\log (x)) \log \left (x^2\right )}{x}+\frac {2 \log (x) \log \left (x^2\right )}{x}-\frac {\log ^2\left (x^2\right )}{2 x}+\frac {(1-\log (x)) \log ^2\left (x^2\right )}{2 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 27, normalized size = 0.87 \begin {gather*} \frac {e^{25-x}}{5}-\frac {\log (x) \log ^2\left (x^2\right )}{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. \(142\) vs.
\(2(26)=52\).
time = 1.54, size = 143, normalized size = 4.61
method | result | size |
default | \(-\frac {\ln \left (x \right ) \left (\ln \left (x^{2}\right )-2 \ln \left (x \right )\right )^{2}}{2 x}-\frac {\left (\ln \left (x^{2}\right )-2 \ln \left (x \right )\right )^{2}}{2 x}-\frac {2 \ln \left (x \right )^{2}}{x}-\frac {4 \ln \left (x \right )}{x}-\frac {4}{x}-\frac {2 \ln \left (x \right )^{3}}{x}-\frac {2 \ln \left (x \right ) \left (\ln \left (x^{2}\right )-2 \ln \left (x \right )\right )}{x}-\frac {2 \left (\ln \left (x^{2}\right )-2 \ln \left (x \right )\right )}{x}-\frac {2 \ln \left (x \right )^{2} \left (\ln \left (x^{2}\right )-2 \ln \left (x \right )\right )}{x}+\frac {40+5 \ln \left (x^{2}\right )^{2}+20 \ln \left (x^{2}\right )}{10 x}+\frac {{\mathrm e}^{-x +25}}{5}\) | \(143\) |
risch | \(-\frac {2 \ln \left (x \right )^{3}}{x}+\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (\mathrm {csgn}\left (i x \right )^{2}-2 \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )+\mathrm {csgn}\left (i x^{2}\right )^{2}\right ) \ln \left (x \right )^{2}}{x}+\frac {\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{2} \left (\mathrm {csgn}\left (i x \right )^{4}-4 \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )+6 \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{2}-4 \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{3}+\mathrm {csgn}\left (i x^{2}\right )^{4}\right ) \ln \left (x \right )}{8 x}+\frac {{\mathrm e}^{-x +25}}{5}\) | \(154\) |
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. 105 vs.
\(2 (27) = 54\).
time = 0.27, size = 105, normalized size = 3.39 \begin {gather*} -\frac {1}{2} \, {\left (\frac {\log \left (x^{2}\right )^{2}}{x} + \frac {4 \, \log \left (x^{2}\right )}{x} + \frac {8}{x}\right )} \log \left (x\right ) + 2 \, {\left (\frac {\log \left (x^{2}\right )}{x} + \frac {2}{x}\right )} \log \left (x\right ) + \frac {\log \left (x^{2}\right )^{2}}{2 \, x} - \frac {2 \, {\left (\log \left (x\right )^{2} + 4 \, \log \left (x\right ) + 6\right )}}{x} + \frac {4 \, {\left (\log \left (x\right ) + 2\right )}}{x} + \frac {2 \, \log \left (x^{2}\right )}{x} + \frac {4}{x} + \frac {1}{5} \, e^{\left (-x + 25\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 21, normalized size = 0.68 \begin {gather*} -\frac {10 \, \log \left (x\right )^{3} - x e^{\left (-x + 25\right )}}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 14, normalized size = 0.45 \begin {gather*} \frac {e^{25 - x}}{5} - \frac {2 \log {\left (x \right )}^{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 21, normalized size = 0.68 \begin {gather*} -\frac {10 \, \log \left (x\right )^{3} - x e^{\left (-x + 25\right )}}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.27, size = 22, normalized size = 0.71 \begin {gather*} \frac {{\mathrm {e}}^{-x}\,{\mathrm {e}}^{25}}{5}-\frac {{\ln \left (x^2\right )}^2\,\ln \left (x\right )}{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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